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Shashank
Shakuntala devi pre university college, Bangalore
XI PCMCs
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Table of Contents Table of Contents CHAPTER 01: FORCE .............................................................................................. 1 CHAPTER MAP: ........................................................................................................................................... 1 INTRODUCTION: ........................................................................................................................................... 2 Momentum (p): .................................................................................................................................. 2 Newton s 2nd Law of Motion: ........................................................................................................ 2 Newton s 3rd Law of motion: .............................................................................................................. 3 Mass and Weight: .............................................................................................................................. 4 Force: ................................................................................................................................................ 4 Kinds of Forces: ................................................................................................................................ 5 Contact force: ............................................................................................................................... 5 Non contact force: ....................................................................................................................... 6 Characteristic of non contact forces: ........................................................................................... 6 Effects of Force: ........................................................................................................................... 7 Moment of a force and equilibrium .................................................................................................... 7 Translational motion ..................................................................................................................... 7 Rotational motion ......................................................................................................................... 7 Torque (moment of force or Turning effect) ...................................................................................... 7 Factors affecting turning effect (Torque): ..................................................................................... 7 Clockwise and anticlockwise moments: ....................................................................................... 8 Couple ............................................................................................................................................... 8 Equilibrium of Bodies:........................................................................................................................ 8 Conditions for equilibrium:............................................................................................................ 8 Kinds of equilibrium: .......................................................................................................................... 9 Static equilibrium: ......................................................................................................................... 9 Dynamic Equilibrium: ................................................................................................................... 9 Principle of moments: ........................................................................................................................ 9 Centre of Gravity (C.G.): ................................................................................................................... 9 Centre of gravity of some regular bodies: ......................................................................................... 9 Uniform Circular Motion (UCM): ...................................................................................................... 10 Differences: ..................................................................................................................................... 10 Review Questions: ................................................................................................................. 12 Numericals: ............................................................................................................................ 13 Application type: .................................................................................................................... 15 Miscellaneous: ....................................................................................................................... 17 Previous Board Questions: .................................................................................................... 19 Answers: ................................................................................................................................ 20 CHAPTER 02: WORK, ENERGY AND POWER ..................................................... 22 Work: ............................................................................................................................................... 22 Expression for work done (W = FS cos ): ................................................................................ 23 Work done under different conditions: ....................................................................................... 23 Energy: ............................................................................................................................................ 24 Definition: ................................................................................................................................... 24 Units: .......................................................................................................................................... 24 Forms of Energy and their sources: ................................................................................................ 25 Types of Energy .............................................................................................................................. 25 Solar Energy:.............................................................................................................................. 25 Heat Energy: .............................................................................................................................. 25 Light Energy: .............................................................................................................................. 25 Volume 1 of 2 Universal Tutorials X ICSE Physics Chemical energy: ....................................................................................................................... 25 Hydro Energy: ............................................................................................................................ 25 Electrical Energy: ....................................................................................................................... 25 Nuclear Energy:.......................................................................................................................... 25 Geothermal Energy: ................................................................................................................... 26 Wind Energy: .............................................................................................................................. 26 Mechanical Energy: .................................................................................................................... 26 Types of Mechanical Energy: .......................................................................................................... 26 Potential Energy: ........................................................................................................................ 26 Derivation: .................................................................................................................................. 26 Derivation: .................................................................................................................................. 26 Relation between kinetic energy and momentum: ..................................................................... 27 Work Energy Theorem: .............................................................................................................. 27 Law of Conservation of Energy: ...................................................................................................... 28 Energy Transformations: ............................................................................................................ 28 Power: ............................................................................................................................................. 29 Definition: ................................................................................................................................... 29 Unit: ............................................................................................................................................ 29 Conversions: .............................................................................................................................. 29 Expression of Power: ................................................................................................................. 29 Energy sources and production of Electricity: ................................................................................. 30 Judicious use of energy: ............................................................................................................ 30 Production of Electricity: .................................................................................................................. 30 Solar Cell: ................................................................................................................................... 30 Solar power plant ....................................................................................................................... 31 Wind energy: .............................................................................................................................. 31 Hydro Electricity: ........................................................................................................................ 31 Nuclear Energy:.......................................................................................................................... 32 Typical Solved Exercises: ...................................................................................................... 33 Review Questions: ................................................................................................................. 34 Numericals: ............................................................................................................................ 34 Application type: .................................................................................................................... 37 Miscellaneous: ....................................................................................................................... 39 Previous Board Questions: .................................................................................................... 41 Answers: ................................................................................................................................ 43 CHAPTER 03: MACHINES ..................................................................................... 48 Definition: ................................................................................................................................... 48 Uses of Simple Machines:.......................................................................................................... 48 Important Definitions: ................................................................................................................. 48 Types of Machines: ......................................................................................................................... 49 Levers:........................................................................................................................................ 49 Types of levers: ............................................................................................................................... 50 Mechanical Advantage of Levers: .............................................................................................. 50 Examples of each class of levers as found in the human body: ..................................................... 50 Inclined Plane: ................................................................................................................................. 50 Mechanical Advantage of Inclined Plane ................................................................................... 50 Pulleys: ............................................................................................................................................ 50 Single fixed pulley ...................................................................................................................... 51 Single Movable Pulley: ............................................................................................................... 51 Combination of pulleys: .............................................................................................................. 51 Block and Tackle System of Pulleys: .............................................................................................. 52 Gears: .............................................................................................................................................. 52 Universal Tutorials X ICSE Physics Volume 1 of 2 Table of Contents Review Questions: ................................................................................................................. 53 Numericals: ............................................................................................................................ 54 Application type: .................................................................................................................... 57 Miscellaneous: ....................................................................................................................... 60 Previous Board Questions: .................................................................................................... 63 Answers: ................................................................................................................................ 66 CHAPTER 04: REFRACTION AT PLANE SURFACE ............................................ 69 Refraction: ....................................................................................................................................... 69 Laws of Refraction: .................................................................................................................... 70 Refractive Index ( ) .................................................................................................................... 70 Refraction through a Glass Slab: .................................................................................................... 71 Critical Angle: .................................................................................................................................. 72 Factors Affecting Critical Angle: ................................................................................................. 72 Total Internal Reflection: ................................................................................................................. 72 Relation between refractive index and critical angle: ................................................................. 72 Applications of Total Reflection: ................................................................................................. 72 Refraction through Prism:................................................................................................................ 73 Total Reflecting Prism: .................................................................................................................... 74 Total internal reflection and different prisms: ............................................................................. 75 Differences between total internal reflection and ordinary reflection ......................................... 75 Review Questions: ................................................................................................................. 75 Numericals: ............................................................................................................................ 77 Application type: .................................................................................................................... 78 Miscellaneous: ....................................................................................................................... 81 Previous Board Questions: .................................................................................................... 83 Answers: ................................................................................................................................ 86 CHAPTER 05: REFRACTION THROUGH A LENS ................................................ 90 CHAPTER MAP: ......................................................................................................................................... 90 REFRACTION THROUGH A LENS: ................................................................................................................. 90 Action of Lens as a Prism:............................................................................................................... 91 Important Definitions: ...................................................................................................................... 91 Ray Diagrams: ................................................................................................................................. 92 Principal Rays in constructing Ray diagram: ............................................................................. 92 Power of lens: .................................................................................................................................. 95 Limitations of the Eye: ..................................................................................................................... 96 SIMPLE MICROSCOPE (MAGNIFYING GLASS): ............................................................................................. 96 Determination of focal length of convex lens: ................................................................................. 96 Uses of lenses: ........................................................................................................................... 97 Typical Solved problems: ........................................................................................................... 97 Review Questions: ................................................................................................................. 98 Application type: .................................................................................................................... 99 Miscellaneous: ..................................................................................................................... 101 Previous Board Questions: .................................................................................................. 103 Answers: .............................................................................................................................. 104 CHAPTER 06: SPECTRUM .................................................................................. 106 CHAPTER MAP: ....................................................................................................................................... 106 DEVIATION: ............................................................................................................................................. 106 Factors on Which Angle of Deviation ( )Depends: .................................................................. 106 Volume 1 of 2 Universal Tutorials X ICSE Physics DISPERSION OF LIGHT: ............................................................................................................................ 107 Recombination of White Light: ...................................................................................................... 107 Prism itself produces no colour: ............................................................................................... 107 Electromagnetic Spectrum: ...................................................................................................... 108 Properties and uses of Different Radiations of electromagnetic spectrum: .................................. 108 Gamma rays: ............................................................................................................................ 108 X-rays: ...................................................................................................................................... 108 Ultraviolet rays:......................................................................................................................... 108 Visible light: .............................................................................................................................. 109 Infrared Radiations: .................................................................................................................. 109 Microwaves: ............................................................................................................................. 109 Radio waves: ............................................................................................................................ 109 ELECTROMAGNETIC SPECTRUM: .............................................................................................................. 110 Common properties of electromagnetic waves ........................................................................ 111 Scattering of Light: ........................................................................................................................ 111 Effects of Scattering: ..................................................................................................................... 111 Blue colour of sky: .................................................................................................................... 111 White colour of sky at noon: ..................................................................................................... 111 Review Questions: ............................................................................................................... 112 Numericals: .......................................................................................................................... 113 Application type: .................................................................................................................. 113 Miscellaneous: ..................................................................................................................... 115 Previous Board Questions: .................................................................................................. 116 Answers: .............................................................................................................................. 116 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 01: Force 1 Chapter 01: Force Chapter Map: Force Introduction Definition Units Absolute units Gravitational units Effects of force Kinds of force Contact Non Contact Momentum Definition Units Relation between Force and Momentum Newton s 2nd Law Derivation F = ma Graphical Representation Newton s 3rd law of motion Mass and Weight Comparison between Mass and Weight Moment of force and Equilibrium Translational Motion Rotational Motion Torque Explanation Factors affecting torque Couple Equilibrium of bodies Kinds of equilibrium Centre of Gravity C.G. of regular bodies UCM Volume 1 of 2 Universal Tutorials X ICSE Physics 1 2 Introduction: Everybody has a property by virtue of which it resists change. This is called inertia. It depends on mass of the body. More the mass more is the inertia. According to Newton s 1st law, Everybody continues to remain in its state of rest or uniform motion along a straight line unless an external unbalanced force is applied. Momentum (p): If two bodies with different masses are moving with the same velocity, then more force is needed to stop the heavier body. Similarly if two bodies with same mass are moving with different velocities, more force is needed to stop the body moving with greater speed. Thus the force required depends on both mass and velocity. Definition: z The product of mass and velocity is called Linear momentum. z Formula: p = mv z It is a vector quantity. z It is in the same direction as applied force. z Units: kg ms 1 or g cm s 1 If the same force is applied for the same interval of time on two bodies of different masses, lighter body moves faster but both have same momentum. Hence force is related to the change in linear momentum. Note: The product of force and time is called impulse. Relation between Rate of Change of Momentum and Force: z Change in momentum p = (mv); If mass (m) is constant, p = m v; Rate of change in momentum is obtained by dividing change in momentum p by time interval t. p v =m t t z But v p is acceleration i.e. rate of change in velocity. Hence = ma t t z F P or F = ma (When mass is constant) t Newton s 2nd Law of Motion: The rate of change of momentum is directly proportional to the force applied on it and this change takes place in the direction of force From Newton s 2nd law, r r p F or F a. Hence, F = ma [Since, mass is constant] [in vector form F = m.a ] t Change in momentum p = (mv) = m v In case of atomic particles moving with velocities comparable to the velocity of light (3 108ms 1), the mass does not remain constant. 2 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 01: Force 3 m0 It increases with velocity (m = 2 1 v 2 where m0 is rest mass) c In such a case p = (mv) The relation, p = m v is true only for small velocities i.e. of the order of 106 or less because at such small velocities, the change in mass is not perceptible. However the relation, p = (mv) is always true. Derivation of F = ma Let F be the applied force on a body of mass m for a time t. Let the velocity of the body change from u to v. Then, Initial momentum p1 = mu; Final momentum p2 = mv. Change in momentum of the body, p2 p1 = mv mu; p = m (v u) z z z z z Rate of change of momentum, z From Newton s 2nd law p m ( v u) t = t p t F = K ma but K = 1 in SI system F m ( v u) or F ma, t F = ma (derived) F Graphical representation of Newton's second law of motion: z When force is constant, a 1 m z When mass is constant, a F z When acceleration is constant, F m i) ii) a iii) a 1/m m F F m p m m0 O iv) a 0.01 C 0.1 C Velocity C Graph showing variation of mass with velocity O 0.01 C 0.1 C Velocity Graph showing variation of momentum with velocity Newton s 3rd Law of motion: For every action, there is an equal and opposite reaction. Volume 1 of 2 Universal Tutorials X ICSE Physics 3 4 Mass and Weight: Mass is the amount of matter present in a body or measure of inertia of the body It is a scalar quantity. The force with which a body is attracted towards the surface of the earth is called its weight on earth. It is a vector quantity (Directed towards the centre of earth. Weight of a body depends on acceleration due to gravity (g) at a given place and the mass of the body. When a force is applied on a body, such that it moves with certain acceleration, then the ratio between force applied and acceleration produced is called inertial mass. If the same force is applied to two bodies of masses m1 and m2 and the acceleration produced is a1 and a2 m a respectively, then 1 = 2 ; (F = m1a1 = m2a2) m2 a1 Thus the ratio of masses is independent of the applied force. For the same applied force, bodies of different masses will have different acceleration. Hence mass of the body gives a measure of its inertia. Thus mass is an intrinsic property of the body. Note: A freely falling body has zero weight during its flight. Weight is zero at the centre of earth, since g = 0 at the centre of the earth. Acceleration due to gravity (g): z It is the acceleration of a body under free fall due to earth s gravity. It is different at different places on earth. It is minimum at the equator and maximum at the poles. It deceases with altitude and depth g does not depend on the mass of the body. Comparison of Mass and Weight: Mass It is the quantity of matter present in a body It is a scalar quantity It is measured by a physical balance It is a constant quantity for a given body. It is measured in g or kg Weight It is the force with which the earth attracts the body. It is a vector quantity It is measured by a spring balance It is a variable quantity and depends on the value of acceleration due to gravity, at a place. It is measured in newton, dyne, kgf, gf. Equations of Motion: i) v = u + at ii) S = ut + at2 iii) v2 u2 = 2as z For uniformly accelerated motion, a graph plotted for speed against time is a straight line. The slope gives acceleration. The area enclosed by the graph with time axis gives distance travelled by the body in that time interval. Force: Definition: z It is that physical cause which changes or tends to change the state of rest or the state of uniform motion of a body. 4 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 01: Force 5 Absolute units of force: z SI : newton (N) ; c.g.s. unit : dyne (dyn) Definition: z The force is said to be 1 newton, if it produces an acceleration of 1 ms 2 in a body of mass 1 kg. i.e., 1 N = 1 kgms2. z The force is said to be 1dyne, if it produces an acceleration of 1 cms 2 in a body of mass 1g z Newton and dyne are called absolute units of force i.e. 1 dyne = 1 g cms 2. Gravitational Unit of force: Definition: z If the acceleration produced by a force acting on a unit mass is equal to the acceleration due to gravity g of the earth, the force is called gravitational force. z Kilogram force (kgf) and gram force (gf) are the gravitational units of force. Definition: z 1 Kgf is the force with which the earth attracts a mass of 1 kg z 1 gf is the force with which the earth attracts a mass of 1 g z 1 gf = 1 g 980 cm s 2 = 980 dyne. z 1 Kgf = 1 kg 9.8 ms 2 = 9.8 N Relation between SI and C.G.S unit of force: z 1N = 1 kg 1 m s 2 = 1000 g 100 cm s 2 = 105 g cm s 2 = 105 dyne. Kinds of Forces: Contact force: Definition z The forces which act on bodies when they are in physical contact are called contact forces. Examples: Frictional force: It is a force which acts on a body in a direction opposite to the direction of motion of the body. It acts parallel to the surfaces in contact. It is a resistive force. Normal reaction force Volume 1 of 2 A force exerted by a surface on a body, normal to surface is called normal reaction Normal reaction is equal and opposite to the weight of body. An object placed on a horizontal surface, does not because the normal reaction balances the weight of body. Universal Tutorials X ICSE Physics the N the fall the Surface W 5 6 Tension force applied through strings: The force exerted by the string on a body tied to it is called tension force Tension force acts upwards and balances the weight of the body under equilibrium condition T W Force by a spring: The force exerted by an elongated spring or compressed spring is called force by a spring. This force is directly proportional to the displacement produced in the spring. It acts opposite to the direction of displacement and tries to bring the spring back to its original position. Hence it is called restoring force. A spring balance works on the principle that restoring force is directly proportional to the displacement Force due to collision: When two bodies collide, an equal and opposite force acts on each body. This force is called force due to collision. This force makes the two bodies to move apart or move together or come to rest under different conditions. Non contact force: Definition: z The force experienced by bodies without being in contact are called non contact forces. Examples Gravitational force: Every particle in the universe attracts every other particle. This force of attraction is called gravitational force. This force depends on their masses and the distance between them. The force on a body due to earth s attraction is called force of gravity. Even though we exert a force on earth, the earth is not moving towards us due to its large mass (inertia). Electrostatic force: The force between two electric charges separated by a distance is called electrostatic force. Like charges repel and unlike charges attract. Magnetic force: The force between two magnetic poles separated by a distance is called magnetic force. Like poles repel and unlike poles attract. Characteristic of non contact forces: They may be attractive or both attractive and repulsive in nature. They depend directly on the product of mass or charges or pole strength. They are inversely proportional to the square of the distance of separation between them. 6 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 01: Force 7 Effects of Force: It can change the speed of a moving body. It can change the direction of motion. It can change the shape of a body. It can move or stop a body. A force applied on a rigid body does not change the inter spacing between the molecules. Hence it produces motion in it (i.e. the body moves). When a body moves, acceleration is produced in it. Hence its velocity changes. As force has both magnitude and direction, it is a vector quantity. A force applied on a non rigid body changes its dimensions (changes shape) because the interspacing between the molecules changes and can also produce motion in it. Moment of a force and equilibrium Translational motion When a force is applied on a stationary object which is free to move, it gets displaced along a linear path. Such a motion is called linear or translational motion. Rotational motion When a body moves about an axis, the motion is called rotational motion Torque (moment of force or Turning effect) The turning effect of force acting on a body about an axis is called the moment of force or torque. F Torque is a vector quantity. A Explanation: O Axis P (FP line of action of force) z Consider a rigid body (A) z As the body A is fixed at O, it does not move in a straight line but it can rotate about O on the application of force. z The line/direction along which the force acts is called the line of action of force. z Due to this force, the body rotates in anticlockwise direction. z The moment of force is equal to the product of magnitude of force and the perpendicular distance of the line of action of force from the axis of rotation. Torque (T) = F distance OP z SI unit is newton metre (Nm) z It is a vector quantity. Factors affecting turning effect (Torque): Magnitude of applied force (greater the force, greater is the torque) Perpendicular distance of line of action of force from the axis of rotation (greater the distance, greater is the torque) Volume 1 of 2 Universal Tutorials X ICSE Physics 7 8 Clock kwise and d anticloc ckwise moments: m T The direction n of turning depends on (i) point of ap pplication of force f and (ii) direction of force If the turning g effect produced is in anticlockwise direction, it is called an nti clockwise moment. A Anticlockwis se moment is taken as positive. B If the turnin ng effect pr roduced is in clock wise w d direction, it is s called cloc ckwise mome ent. Clockwise m moments ar re taken as negative. n F Cloc ckwise Anticlockwise e xamples Ex i) Steering S whe eel ii) Bicycle B whee el iii) See saw iv) Spanner Coup ple Def finition: z Two equa al, opposite and parallel forces not acting a along the same line e on a body fr ree to turn ab bout a point form a couple. Note: : The two fo orces do not cancel each h other beca ause their lin ne of action n is not same e. A F d O (axis) F z Moment of o a couple is equal to the t product of either of the forces a and the perp pendicular distance between b the lines of actio on of the forc ces. z Moment of o couple = F d (ref. dia agram) Equi ilibrium of Bodies: If se everal forces s acting on a body do no ot change its state of rest or of motio on, the body is said to be in equilibrium m. Cond ditions for r equilibr rium: T The resultant t of all forces s acting on th he body shou uld be equal to zero. The T resultant t moment of all forces ac cting on the body b about th he point of ro otation should be zero 8 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 01: Force 9 Kinds of equilibrium: Static equilibrium: When a body remains in the state of rest under the influence of the applied forces, the body is in static equilibrium. Dynamic Equilibrium: When a body remains in the state of motion under the influence of the applied forces, the body is in dynamic equilibrium. Principle of moments: In equilibrium, the sum of clockwise moments is equal to the sum of anti clockwise moments L2 L1 Note: Physical balance works on principle of moments W1L1 = W2L2 F W1 W2 Where, W1 & W2 are the weights and L1 & L2 are their distances from the fulcrum. (force arms) Centre of Gravity (C.G.): It is the point through which the entire weight of the body acts and the algebraic sum of moments of weights of particles constituting the body is zero Position of C.G. of a body depends on its shape i.e. on the distribution of mass in it. C.G. may lie within the material of the body or outside the material of the body. W W W W W W W C. G W W Note: C.G. of a ring or hollow sphere lies at its centre. Centre of gravity of some regular bodies: Object Rod (uniform) Position of C.G C.G mid point Circular disc Geometric centre Sphere Geometric centre cylinder mid point on the axis Volume 1 of 2 Universal Tutorials X ICSE Physics 9 10 Object Position of C.G Solid cone h 4 h 3 hollow cone at. 1/4 height from the base, on the axis at 1/3 height from the base, on the axis circular Ring centre of the ring (outside the ring) Triangular lamina Intersection of medians (centroid) Parallelogram Intersection of diagonals Note: When a body is suspended freely it rests in such a way that C.G. lies below the point of suspension. Uniform Circular Motion (UCM): When a body moves with constant speed in a circular path, it is said to perform uniform circular motion. V In UCM, speed is constant but velocity (i.e. direction) changes. Hence it is an accelerated motion. In uniform linear motion speed and direction are constant. Hence acceleration is zero. V In UCM, the change in direction is due to the force called centripetal force. Centripetal force is the force acting towards the centre of the circular path of body. Centripetal force is a real force because it has a cause/ source. The apparent force acting away from the centre of a circular path is called centrifugal force. It is a virtual or fictitious force. V V Note: If while moving in a circular path, the string is cut off the particle will move along the tangent to the path and not along a line containing the centre. Differences: 1) (a) uniform circular and uniform linear motion. (b) Centripetal force and centrifugal force. Ans: a) Uniform circular motion Velocity changes. It is an accelerated motion. 10 Uniform linear motion Velocity is constant. Its acceleration is zero. Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 01: 0 Force 11 b) Centripetal force C f T force dire The ected toward ds the centre e of a circular path h is called ce entripetal forc ce. Centri ifugal force ch acts away y from It is the force whic the centre of a circ cular path 2) Ob bserve the given g diagra am and answ wer the questions given n below: a) When the mer rry go round d starts rota ating what is s the observatio on of the pe erson standi ing at M. Ans: Th he person fin nds the ball is moving in n a circular path p be ecause the tension in the string g provides the ne ecessary cen ntripetal force e. b) What is the observation o g at of the person standing A on the merr ry go round? Ans: Th he person at t A funds tha at the ball is stationary at a P be ecause when n the merry go g round rota ates, two for rces are e acting on the ball. One O is tensio on in the string tow wards the centre c and centrifugal c fo orce away fr rom the e centre. Since both th hese forces one equal and a op pposite the ne et force is ze ero. Hence th he ball is stat tionary. c) What would th heir observa ations be if the string is s cut off? Ans: Fo or the person n at M, tension has ceased. Hence there is no centripetal fo force. The ba all moves tan ngential alon ng the path P1, P11, P111 etc. For th he person on n the merry go round, the ball is alw ways in front t of him i.e. at a P when he e is at A, at P1 when he is i at A1 etc. So it appear rs that the ba all is moving because of centrifugal c fo orce acting aw way from the e centre. Typ pical Solve ed Problems: 1) Ca alculate the change in momentum m of a car wei ighing 1400 kg, when it ts speed 1 1 (a) ) increases from 36 kmh to 72 km mh uniform mly, (b) decre eases from 20 ms 1 to 5 ms 1. Sol: a) Given m = 1400 kg 5 1 1000 ms 1 = 10 ms 1 (1 ( km h 1 = m s 1) u = 36 km h 1 = 36 60 0 60 1 18 1 1000 v = 72 km h 1 = 72 ms 1 = 20 ms 1 60 0 60 Change in velocity v = (20 0 10) ms 1 = 10 ms 1 change in momentum m = mass change c in velocity = 1400 0 10 = 14, 0 000 kg ms 1 b) Change in momentum m = mass cha ange in veloc city 1 = 1400 kg (5 20) ms = 140 00 ( 15) kg g ms 1 = 21,000 kg ms 1 1 m 500 g travels with h a uniform velocity of f 25 ms for r 5s. The br rakes are 2) A toy car of mass a the car is uniformly y retarded and a comes to rest in fur rther 10s. Ca alculate then applied and a) the retardation ce which the e car travels s after the br rakes are ap pplied b) the distanc xerted by br rakes c) the force ex u = 25 ms Sol: a) m = 500 g = 0.5 kg s 1, v=0 t = 10 sec 0 25ms 1 v u 2 = = 2.5 ms 2 t 10s overed S = ut + at2 b) Distance co S = (25) (10 0) + ( 2.5) (10)2 = 250 125 = 125 m c) Force F = ma m = 0.5 2.5 5 N = 1.25 N a= Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 11 12 3) The weight of a standard mass of 1 kg is found to be 1.7 N when it is measured on the moon s surface using a spring balance. Another object of unknown mass M suspended from the same spring is found to weigh 6.8 N on the moon. What is the mass of the unknown object? Sol: m = 1 kg, w = 1.7 N and W = 6.8 N, M = ? Since weight is proportional to the mass, m w = M W 1 1 .7 = M = 4 kg M 6 .8 4) The moment of a force of 10 N about a fixed point is 5 Nm. Calculate the distance of the fixed point from the line of action of the force. Sol: moment of force (T) = 5 Nm. Force (F) = 10 N. Distance (d) = ? 5 = 0.5 m. 10 5) A uniform metre rule is pivoted at its mid point. A weight of 50 gf is suspended at one end of it. Where should a weight of 100 gf be suspended to keep the rule horizontal? Sol: Since the rule is a metre rule, its length is 100 cm. 50 cm O 50 cm midpoint is 50 cm (fulcrum) x F When 50gf is suspended on one side, the rule will tilt on that side. Hence, the 100 gf should be suspended 100 gf 50 gf on the other side of fulcrum. By principle of moments, sum of anticlockwise moments = sum of clockwise moments T=F d 5 N m = 10 N d d= W1L1 = W2L2 50 gf 50 cm = 100 gf x x= 50 50 cm. 100 x = 25 cm from 50 cm mark i.e. at 75 cm mark of the rule. REVIEW QUESTIONS: Direct questions: 1) What are contact forces? Give two examples. 2) What are non-contact forces? Give two examples. 3) Classify the following as contact and non-contact forces. a) frictional force b) normal reaction force c) force of tension in a string d) gravitational force e) electric force f) magnetic force. 4) State one factor on which the magnitude of a non-contact force depends. How does it depend on the factor stated by you? 5) Define the term force . 6) State the effects that a force can produce. Give one example of each effect. 7) Name two effects of a force applied to a non rigid body. 8) A force is applied on (i) a non-rigid, and (ii) a rigid body. How does the effect of the force differ in the two cases? 9) Give one example in each of the following cases a) A force stops a moving body. b) A force causes motion of body. c) A force produces change in size of the body. d) A force produces change in shape of the body. 12 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 01: Force 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 13 Define the term linear momentum. State its S.I. unit. Define newton (the S.I. unit of force). Write down the gravitational unit of force. How is it related to newton? State the condition when a force produces a) translational motion in a body b) rotational motion in a body Define moment of force and state its S.I. unit. Is moment of a force a scalar or a vector? State two factors on which moment of force about a point depends. Why is it easier to open a door by applying the force at the free end of it? The stone of hand flour grinder is provided with a handle near its rim. Give a reason. It is easier to turn the steering wheel of a large diameter than that of a small diameter. Give reason. Draw a neat labelled diagram to show the direction of two forces acting on a body to produce rotation in it. Also mark the point about which rotation takes place, by the letter O. Define moment of couple. Write its S.I. unit. State the condition when a body is in (i) static equilibrium and (ii) dynamic equilibrium. Give one example for each. State the principle of moments. Give one device as application of it. Can the centre of gravity be situated outside the material of the body? Give an example. Define the term centre of gravity of a body . Which of the following quantity remains constant in a uniform circular motion? a) velocity b) acceleration c) speed d) force. Name the force required for circular motion. State its direction. What is centripetal force? Figure shows three pieces of card board of uniform thickness cut into different shapes. On each diagram draw two lines to locate the position of centre of gravity, G. Is it possible to have an accelerated motion with a constant speed? Name such type of motion. Differentiate between a uniform linear motion and a uniform circular motion. Is centrifugal force the force of reaction of centripetal force? Is centrifugal force a real force? NUMERICALS: Class Work: 1) Two balls of masses in ratio 1:2 are dropped from the same height. Find: a) the ratio between their velocities when they strike the ground, and b) the ratio of the forces acting on them during motion. [a) 1:1 (b) 1:2] 1 2) A body X of mass 5 kg is moving with velocity 20 ms while another body Y of mass 20 kg is [1:1] moving with velocity 5 m s 1. Compare the momentum of the two bodies. 1 3) A toy car of mass 500 g travels with a uniform velocity of 25 ms in 5 s. The brakes are then applied and the car is uniformly retarded and comes to rest in further 10 s. Calculate: i) the retardation ii) the distance which the car travels after the brakes are applied. iii) the force exerted by the brakes. [(i) 2.5 ms 2 (ii) 125 m (iii) 1.25 N] 4) A nut is opened by a wrench of length 10 cm. If the least force required is 50 N, find the moment of force needed to turn the nut. [0.5 Nm] Volume 1 of 2 Universal Tutorials X ICSE Physics 13 14 5) A wheel of dia ameter 2 m is s shown in with w axle at 0. 0 A force F = 2 N is app plied at B in the dire ection shown in figure. Calculate C the e moment of f force about (i) ce entre 0, and (ii) ( point A. [(i) 2Nm (clockwise) ( (ii) 4 Nm (clo ockwise) 6) Tw wo forces ea ach of magni itude 10 N act a vertically upwards an nd downward ds respective ely on the tw wo ends of a uniform ro od of length 4 m which is pivoted at a its mid po oint as show wn in fig. De etermine the magnitude of o resultant moment m of fo orces about the pivot O. [40 Nm (clock wise)] 7) A uniform metre rule is piv voted at its mid-point. m A weight w of 50 0 gf is suspen nded at one end of it. Where should a weight of 100 1 gf be suspended to keep k the rule e horizontal? [25 5 cm from oth her end] 8) Th he diagram below sho ows a unifo orm bar su upported at th he mid point O. A weight t of 40 gf is placed at a distance 40 cm to the le eft of the oint O. How can you bal lance the ba ar with a po we eight of 80 gf f? [Place e 80 gf at 20 0 cm to the rig ght of O] 9) A uniform mete er rule of we eight 10 gf is pivoted at its s 0 mark. (i) What mome ent of force depresses d the e rule? (ii) Ho ow can it be made horizo ontal by applying a least force? [ 500 gf cm [(i) m (ii) by force e of 5 gf upw wards at 100 cm c mark] 10) A uniform met tre rule of ma ass 100 g is s balanced on a fulcrum at mark 40 c cm by suspe ending an un nknown mass s m at the mark m 20 cm. Find the va alue of m. To o which side the rule will tilt if the ma ass m is mo oved to the mark 10 cm m? What is the resultan nt moment now? How can it be [m = 50 g at 50 cm ba alanced by an nother mass 50 g? c mark.] Home Work: W 1) A car of mass 600 kg is mo oving with a speed of 10 ms 1 while a scooter of m mass 80 kg is moving 1 wit th a speed of o 50 ms . Compare their momentum m. Which vehicle will requ uire more forc ce to stop [3:2, car] it in the same interval i of tim me? 2) A body of mas ss 50 g is mo oving with a velocity v of 10 0 ms 1. It is brought b to re est by a resis stive force of 10 N. Find : i) the retar rdation and ii) i the distan nce that the body will tra avel after the e resistive for rce is applied d. [(i) 200 ms 2 (i ii) 25 cm] 3) Th he moment of o a force of 10 1 N about a fixed point 0 is 5 N m. Calculate C the e distance of f the point [0.5 m] 0 from f the line of action of the force. 4) Th he diagram in n Fig. shows s two forces F1 = 5 N an nd F2 = 3 N acting at po oints A and B of a rod piv voted at a po oint 0, such that OA = 2 m and OB = 4 m. Ca alculate i) Moment M of fo orce F1 abou ut O. ii) Moment of force f F2 abou ut O iii) Total mome ent of the two o forces abou ut O. [i) 10 Nm (antic clockwise) (ii i) 12 Nm (clo ock wise) (iii) 2 Nm (clock kwise)] 5) Fig g Shows tw wo forces ea ach of magn nitude 10 N acting at th he po oints A and B at a separa ation of 50 cm, c in oppos site directions. Ca alculate the resultant r moment of the two t forces about a the point (i) A, (ii) B and d (iii) O, situ uated exactly y at the midd dle of the tw wo for rces. [(i) 5 Nm clock kwise (ii) 5 Nm clockwise e (iii) 5 Nm clockwise] 14 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 01: 0 Force 15 6) A steering wh heel of diameter 0.5 m is rotated anticlockwise by applying g two forces s each of ma agnitude 5 N. N Draw a diagram to show the application of for rces and calculate the moment m of [2.5 Nm] co ouple applied d. 7) A uniform met tre rule balances horizon ntally on a knife k edge placed at the 58 cm mark when a we eight of 20 gf f is suspende ed from one end. [105 gf] ii) What i) Draw D a diagr ram of the ar rrangement. W is the weight w of the e rule? 8) Sh hows a unifo orm metre rule placed on n a fulcrum at a its mid-point O and having g a weight 40 0 gf at the 10 cm m mark and a weight of 20 gf at the 90 0 cm mark. i) is the metr re rule in equ uilibrium? If not, n how will the rule turn. ii) How can the rule be br rought in equ uilibrium by using u an additional weigh ht of 40 gf? [(i) No, anticlock wi ise (ii) add 40 0 gf at 70 cm m mark] 9) When a boy weighing w 20 kgf k sits at on ne end of a 4 m long see e-saw, it gets s pushed dow wn at this en nd. How can it be brought t to the horiz zontal positio on by a man weighing w 40 kgf. [1 m from the cen ntre on opposite side] 10) A physical balance has its s arms of len ngth 60 cm and 40 cm. What weigh ht kept in the e pans of lon nger arm will l balance an object of we eight 100 gf kept k on other r pan? [66.679 gf] 11) Th he diagram in Fig. show ws a uniform m metre rule e weighing 10 00 gf, pivoted d at its centr re 0. Two we eights 150 gf g and 250 gf hang from the metre rule as shown. Calculate: (i) ( the total an nticlockwise moment ab bout 0, (ii) the total clockwise mo oment about 0, (iii) the e difference of anticlock kwise and clo ockwise mom ment, and (i iv) the distance from 0 where a 10 00 gf weight should be placed to ba alance the me etre rule. (i) 6000 gf cm (ii) ( 5000 gf cm c (iii) 1000 gf g cm )iv) 10 cm to the rig ght of O.] APPLICATION TYPE: T Class Work: W 1) A, B and C are three force es each of magnitude m 4 N acting in the t plane of paper as sh hown The po oint O lies in the same pla ane. B A i) Which W force has the leas st moment ab bout O? Give e a reason. C O ii) Which force has the grea atest momen nt about O? Give G a reaso on. 2) A body is acte ed upon by two t forces each e of magn nitude F, but t in opposite e directions. State the eff fect of the forces if a) both forces act at the sa ame point of the t body. b) the two forces act at two o different po oints of the bo ody at a separation r. 3) Tw wo objects ha ave masses in the ratio 2 : 1 and velo ocities in the ratio 1 : 3. a) What is the ratio of their r momenta? b) What is the ratio of their r kinetic ener rgy? 4) State the effec ct of force on: (i) Stationary rigid object fre ee to move. (ii) ) Object pivo oted about an n axis. 10 N 2m 5) (i) In the given diagram what is the resu ultant torque? ) Will the obje ect rotate in clockwise or r anticlockwis se direction? ? (ii) 3m 12 Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 15 16 6) State one factor on which the magnitude of non contact force depends. How does it depend on the factor stated by you? 7) In the given diagram, Block m Pulley mark the direction of Tension. Frictionless surface String 8) What is the effect of force on a non rigid body not free to move? 9) On what a factor does the direction of turning produce on a body depends. 10) Give reason: The upper circular stone of a hand flour grinder is provided with a handle near its rim. 11) A spanner has a large handle. Why? 12) What are the conditions for equilibrium? Y 13) The following diagram shows two parallel and opposite forces F1 and F2 each of magnitude 5N, with their lines of action separated by a distance F2 = 5N of 2m. A point X lies midway between F1 and F2 while a point Y lies on 2m X F2. a) Calculate the total moment of the two forces about (i) X and (ii) Y F1 = 5N b) State the effect produced by the two forces about the points X and Y. Home Work: 1) The adjacent diagram shows a heavy roller, with its axle at O, which is to be raised on a pavement XY by applying minimum O X Y possible force. Show by an arrow in the diagram the point of application and the direction in which the force should be applied 2) A small pebble is placed near the periphery of a circular disc which is rotating about an axis passing through its centre. a) What will be your observation when you are standing outside the disc? Explain it. b) What will be your observation when you are standing at the centre of the disc? Explain it. 3) A force is applied on (i) an iron ball (ii) on clay ball (both of same size.). What is the effect on each of them? 4) How does the turning effect change when i) the distance between the point of application of force and the axis of rotation is doubled. ii) the force is reduced to half (other parameters remaining same) 5) In the given diagram, O is the centre of a circular wheel of radius 6 cm. A F1 F1 O is a point on OA such that OO is 3 cm. [O is the axis] O When forces F1 and F2 are applied, the wheel is in equilibrium. O Compare the two forces F1 and F2. Justify. 6) F1 Two blocks of masses m1 and m2 on a horizontal frictionless table are connected by a light spring as shown. Mark the direction of restoring force. (F1 is the applied force) 7) A cylinder hangs from a chord as shown mark the direction of tension. 8) What is the effect of force applied on a moving body when applied? i) perpendicular to the direction of motion. ii) in any direction 9) What is the sign convention for i) clockwise moment ii) anticlockwise moment 16 Universal Tutorials X ICSE Physics W Volume 1 of 2 Chapter 01: Force 17 10) For turning a steering wheel, a force is applied tangentially on the rim of the wheel. Why? 11) Classify as static and dynamic equilibrium i) A book lying on a table. ii) A rain drop reaching the earth with constant velocity. iii) A beam balance held horizontally. 12) The wheel shown in the diagram has a fixed axle passing through O. The wheel is kept stationary under the action of B A F1 i) a horizontal force F1 at A and ii) a vertical force F2 at B. O O a) Show the direction of force F2 in the diagram. b) Which of the force F1 or F2 is greater? c) Find the ratio between the forces F1 and F2. Given : AO = 2.5 cm, BO = 1.5 cm and O O = 2.0 cm. 2) Draw a neat labeled diagram for a particle moving in a circular path with a constant speed. In your diagram show the direction of velocity at any instant. MISCELLANEOUS: 1) Give one example in each case where a) the force is of contact, and b) force is at a distance. 2) Which of the following is not the force at a distance a) electrostatic force b) gravitational force c) frictional force d) magnetic force. 3) Give one example, in each case, of a force that a) lifts b) pushes c) pulls d) stretches e) compresses f) resists. 4) State Newton s first law of motion. Why is it called the law of inertia? 5) Write an expression for the change in momentum of a body of mass m moving with velocity v if (i) v << c and (ii) v = c. State the condition when the change in the momentum of a body depends only on the change in its velocity. 6) State Newton s second law of motion. Under what condition does it take the form F = ma? 7) Complete the following sentences a) Mass change in velocity = ...... time interval. b) The mass of a body remains constant till the velocity of body is . 8) Prove that force = mass acceleration. State the condition when it holds true. 9) Name the S.I. unit of (a) linear momentum, (b) rate of change of momentum. 10) State the relationship between force, mass and acceleration. Draw graphs showing the relationship between a) acceleration and force for a constant mass. b) acceleration and mass for a constant force. 11) A rocket is moving at a constant speed in space by burning its fuel and ejecting out the burnt gases through a nozzle. Answer the following: a) Is there any change in the momentum of the rocket? If yes, what causes the change in momentum? b) Is there any force acting on the rocket? 12) State Newton s third law of motion. 13) Name and define the S.I. and C.G.S. units of force. How are they related? 14) 1 N is the force which produces a) an acceleration of 1 m s-2 on a body of mass 1 g b) an acceleration of 1 cm on a body of mass 1 kg. Volume 1 of 2 Universal Tutorials X ICSE Physics 17 18 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 18 c) an acceleration of 1 cm s 2 on a body of mass 1 g. d) an acceleration of 1 m s 2 a body of mass 1 kg. Explain what is understood by the following statement 1 kilogramme force (kgf) = 9.8 newton. The correct relationship between kgf and N is a) 1 kgf=N b) 1kgf = 9.8N c) 9.8 kgf = 1N d) 1 kgf = 980N Complete the following a) Force = mass x b) 1N = dyne c) 1N = kgf (approx) d) newton is the unit of .. The moment of a force about a given axis depends: a) only on the magnitude of force b) only on the perpendicular distance of force from the axis c) neither on the force nor on the perpendicular distance of force from the axis d) both on the force and its perpendicular distance from the axis. Write the expression for calculating the moment of force about a given axis. The unit of moment of force is: N a) N b) c) kg m2s 1 d) Nm m What do you understand by clockwise moment and anticlockwise moment of forces? Classify them as positive and negative. A spanner (or wrench) has a long handle. Why? In order to rotate a bar pivoted at its mid point, we need to apply: a) a large force at any point on the bar b) a small force exactly at the mid point where it is pivoted c) two unequal forces at the two ends, but in the same direction d) two equal forces at the two ends, but in opposite directions. A body is acted upon by two unequal forces in opposite directions, but not in one line. The effect is that a) the body will have only the rotational motion b) the body will have only the translational motion c) the body will have neither the rotational motion nor the translational motion d) the body will have rotational as well as translational motion. What do you understand by the term couple? State its effect. Give two examples of couple action in our daily life. Prove that, Moment of couple = Force Couple arm. What do you mean by equilibrium of a body? State two conditions for a body acted upon by several forces to be in equilibrium. The appliance which works on the principle of moments, is a) spring balance b) beam balance c) pendulum clock d) balance wheel. On what factor does the position of centre of gravity of a body depend? Explain your answer with an example. What is the position of centre of gravity of a rectangular lamina? At which point is the centre of gravity of a triangular lamina situated? Where is the centre of gravity of a uniform ring situated? A square card board is suspended by passing a pin through a narrow hole at its one corner. Draw a diagram to show its rest position. In the diagram mark the point of suspension by the letter S and centre of gravity by the letter G. Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 01: Force 19 35) Explain how you will determine the position of centre of gravity experimentally for a triangular lamina (or a triangular piece of card board). 36) State whether the following statement is true or false. The position of centre of gravity of a body remains unchanged even when the body is deformed. 37) Explain the meaning of uniform circular motion. Give one example of such motion. 38) Give an example of motion in which speed remains uniform, but the velocity changes. 39) A uniform circular motion is an accelerated motion. Explain. 40) A piece of stone tied at the end of a thread is whirled in a horizontal circle. Name the force which provides the centripetal force. 41) Explain the motion of a planet around the sun in a circular path. 42) State whether the following statements are true or false by writing T/F against them. a) The earth moves around the sun with a uniform velocity. b) The motion of the moon around the earth in circular path is an accelerated motion. c) A uniform linear motion is not accelerated, while a uniform circular motion is an accelerated. d) In a uniform circular motion, the speed continuously changes because the direction of the motion changes. PREVIOUS BOARD QUESTIONS: 1) i) Define 1 kgf. ii) How is it related to the S.I. unit of force? [2012] 2) i) What are non-contact forces? ii) How does the distance of separation between two bodies affect the magnitude of the noncontact force between them? [2012] 3) A boy of mass 30 kg is sitting at a distance of 2 m from the middle of a see-saw. Where should a boy of mass 40 kg sit so as to balance the sea-saw? [2012] 4) i) What is meant by the term moment of force ? ii) If the moment of force s assigned a negative sign then will the turning tendency of the force be clockwise or anticlockwise? [2012] 5) i) Which of the following remains constant in uniform circular motion : speed or velocity or both? ii) Name the force required for uniform circular motion. State its direction. [2012] 6) i) Define one newton. ii) Write the relation between S.I. unit and C.G.S. unit of force. [2011] 7) Where does the position of centre of gravity lie for i) a circular lamina ii) a triangular lamina? [2011] 8) A uniform metre scale can be balanced at the 70.0 cm mark when a mass of 0.05 kg is hung from the 94.0 cm mark. i) Draw a diagram of the arrangement ii) Find the mass of the metre scale. [2011] 9) If m is the mass of the body, v its velocity and p the momentum then write a relationship between change in momentum, mass and velocity of the body when a) v is almost equal to c, the velocity of light b) v is very, very less as compared to c, the velocity of light. (2009) 10) 6.4 kJ of energy causes a displacement of 64 m in a body in the direction of force in 2.5 seconds. Calculate (2009) a) the force applied b) power in horse power (hp) (Take 1 hp = 746 W) 11) Name the S unit of: i) linear momentum Volume 1 of 2 (2008) ii) rate of change of momentum. Universal Tutorials X ICSE Physics 19 20 12) Draw a graph showing the relationship between acceleration and mass for a constant force. y (2006) 13) The speed time graph of a moving car is as shown in 20 m/s B the figure given alongside. Calculate: Speed in m/s i) The distance covered by the car in 5 seconds. A ii) The acceleration of the car. 0 x 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 5 seconds (Time in seconds) Mention any two differences between the mass and weight of a body. (2006) Define newton, the SI unit of force. State its relationship with the C.G.S. unit of force. (2006) State Newton s Second law of motion. (2005) Two balls of mass ratio 1:2 are dropped from the same height. State i) the ratio between their velocities when they strike the ground. ii) ratio of the force acting on them during their motion, (2004) nd State Newton s 2 law of motion both in words and in equation form. Under what condition does this equation be F = ma (2004) The weights of two bodies are 2.0N and 2.0 kgf respectively. What is the mass of each body? (2003) (take g = 10 ms 2) (2002) State the SI unit of momentum of a body What is the weight of a body of mass 12 kg? What is the force acting on it? (g = 10ms 2) (2001) A body of mass 1kg is thrown vertically up with an initial speed of 5 ms 1. What is the magnitude (1997) and direction of force due to gravity on the body at its highest point? (g = 9.8ms 2) (1996) Define SI unit of force. Obtain a relation between SI and cgs unit of force. A body P has a mass of 20 kg and is moving with a velocity of 5 m/s. Another body Q has a mass of 5 kg and is moving with a velocity of 20 m/s. Calculate: (i) The ratio of the momentum of P and Q (ii) the kinetic energy of P in S.I. units. (2000) ANSWERS: Previous Board Questions: 1) i) 1 kgf is the force due to gravity on a mass of 1 kg. ii) 1 kgf = 9.8N 2) i) The forces which are experienced by a body even when it is not physically touched by the other body are called the non-contact forces. ii) The magnitude of the non-contact force decreases as the distance of separation between two bodies increases. 3) Let the boy of mass 40 kg sits at a distance of x in from the middle of sea-saw on other side of the boy of mass 30 kg to balance the sea-saw. Then by principle of moments, 30 2 = 1.5 m 40 Thus the boy of mass 40 kg should sit at a distance 1.5 m from the middle on other side. 4) i) Moment of force means the turning effect of force about an axis. It is equal to the product of magnitude of force and the perpendicular distance of the line of action of force from the axis of rotation. ii) Clockwise. 5) i) Speed. ii) Centripetal force. It is directed towards the centre of circle. 30 kgf 2 m = 40 kgf . x or X = 9) 0.06 kg 10) a) p = (mv) b) p = m v 11) Energy = 6.4 103 = 6400 J; s = 64 m; t = 2.5 s a) Energy = work done = F s 6400 = F 64 F = 100 N 20 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 01: Force b) P = 13) m 21 W 6400 2560 = 2560 W Power in (hp) = = 3.43 HP = t 2.5 746 F 18) 1:1, 1 = 1:2 F2 a 20) Weight of body = 2 N W1 = m1g 2 = m1 10 m1 = 2 = 0.2 kg 10 Weight of body = 2.0 kgf W2 = m2g (2kgf = 2 10N) 2 10 = m2 10 m2 = 20 = 2 kg 10 22) 120 N 23) When the body is at the highest point of its motion, its velocity is zero but it is acted upon by a downward acceleration due to gravity. Thus, it will be acted upon by a force due to gravity in the downward direction. Force = 1 9.8 = 9.8N 24) S.I. unit of force is newton. One newton force is said to be acting on a body of mass 1 kg, if it produces in it an acceleration of 1 ms 2. Thus, 1 newton = 1 kg 1 ms 2 = 1,000 g 100 cm s 2 = 105 g cm s 2 = 105 dyne. 25) ratio is 1 : 1; K.E. = 250 J Volume 1 of 2 Universal Tutorials X ICSE Physics 21 22 Chapter 02: Work, Energy and Power Work Definition Units Expression for work done Work done under different conditions Energy Definition Units Forms of energy Types of Energy Law of Conservation of Energy Examples Simple Pendulum Freely falling body under gravitational force Energy Transformation Power Definition Units Conversions Expression for power Energy source and production of electricity Solar Power plant Wind energy Hydro energy Nuclear energy Work: Definition: z Work is said to be done when a force acting on a body moves it through some distance (i.e. produces displacement). z Work done is a scalar quantity. 22 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 02: Work, Energy and Power 23 The amount of work done depends on: z Magnitude of force applied. z The distance moved by the object. z Magnitude of work done is given by the product of force applied and distance moved in the direction of force (i.e. displacement). W = F S Units: z In c.g.s. system, unit of work is erg. 1 erg = 1 dyn 1 cm z The work done is said to be 1 erg when a force of 1 dyne moves a body by 1 cm in the direction of force. z SI unit of work is joule (J). z 1J=1N 1m Definition: z The work done is said to be 1 joule when a force of 1 newton moves a body by 1 m in the direction of force. 1 J = 1 N 1m = 105 dyn 102 cm = 107 erg. i.e., 1J = 107 ergs Gravitational units of work c.g.s: 1 gf cm = 980 erg 1 kgf m = 9.8 joule Expression for work done (W = FS cos ): Let the object m be initially at A. Let a force F displace it to C but act along AB. C Work (W) = Force AB Displacement S In ABC, m AB cos = AC F A S cos B AB = AC cos = S cos W = F S cos = force component of displacement in the direction of force. Work done under different conditions: Work done is zero z If no displacement is produced by the force. (s = 0) eg. pushing a wall. z If displacement is normal to the direction of force ( = 90 ) eg. A coolie moving with a load along a horizontal surface. If a body is raised to height h . z In such cases work is done to overcome the gravitational attraction of the earth. z W = mgh z It is positive and maximum as = 0 and cos = 1. Volume 1 of 2 Universal Tutorials X ICSE Physics 23 24 z Work done by gravity is mgh whether a person comes by stairs, elevator or an inclined plane. If force and motion are in different directions. z Work done is given by: r r W = F S z W = F S cos . m A m S B When = 0 , W = FS (maximum) When = 90 , W=0 When = 180 W = FS (force and displacement are in opposite direction work done is negative) (minimum) Graphical representation of work done for a variable force: z Area enclosed gives total work done by gravitational force = mgh z Bigger units of work are: 3 1 kilo joule = 10 J 6 1 mega joule = 10 J 9 1 giga joule = 10 J F h Energy: Definition: The capacity or ability to do work is called energy. It is a scalar quantity. When a body does work, energy decreases and when work is done on the body, energy increases. Units: C.G.S. : erg SI : joule Bigger units: watt hour (Wh), kilo watt hour Relation: z Commercial unit of electrical energy is kilo watt hour (kwh) z Definition: 1 kwh is the energy spent by a source of power 1 kw in 1 hour. z 1 kWh = 1 kilowatt 1 hour = 1000 Js 1 3600 s = 3.6 106 J = 3.6 MJ i.e., 1 kWh = 3.6 106 J z Nuclear energy is measured in electron volt (eV)1 eV = 1.6 10 19 J Definition: 1eV is the energy gained by an electron when it is accelerated through a p.d of 1 volt z Heat energy is measured in calorie or kilocalorie 1J = 0.24 cal 1 cal = 4.18 J Definition: 1 cal is the energy required in raising the temperature of 1 g of water from 14.5 C to 15.5 C 24 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 02: Work, Energy and Power 25 Forms of Energy and their sources: Chemical energy Fossil fuels Electrical energy Electric charges Nuclear energy Nucleus of atoms Heat energy Fuels Sound energy Vibrating bodies Light energy Sun, electricity Solar energy Sun Mechanical energy (energy due to state of rest or motion) Types of Energy Solar Energy: The energy radiated by the sun is called solar energy. The earth receives 1 KJ energy per second per meter square area. This energy is produced in the sun by nuclear fusion reaction. Solar energy cannot be used to do work directly because it is diffused and not available uniformly. Solar cells and solar Panels make use of solar energy. Solar cells convert solar energy to electrical energy. Heat Energy: Energy released on burning coal, oil, wood or gas is heat energy. In steam engine, heat energy is converted to mechanical energy. Light Energy: It is the form of energy in presence of which other objects are seen Chemical energy: The energy obtained by burning fossil fuels is called chemical energy. Hydro Energy: The energy possessed by moving/flowing water is called hydro energy. Electrical Energy: When two dry bodies are rubbed together, they get charged due to movement of free electrons from one object to another. This is called electrical energy. Nuclear Energy: The energy released during nuclear fission or fusion reaction is atomic/ nuclear energy Mass gets converted to energy as E = mc2 (Einstein s equation) Volume 1 of 2 Universal Tutorials X ICSE Physics 25 26 Geothermal Energy: The energy released in nuclear disintegrations in the interior of earth is called geothermal Energy. Wind Energy: The energy possessed by fast moving air is called wind energy. Mechanical Energy: Energy possessed by a body due to its state of rest or motion is called mechanical energy. Types of Mechanical Energy: Potential Energy: z The energy possessed by a body due to its position of rest relative to the earth or configuration is called potential energy (PE). Types of PE energy: z Gravitational P.E.: Energy possessed due to its position relative to earth s centre. Eg. water stored in a dam. z Elastic P.E.: Energy possessed due to change in configuration or shape is called Elastic P.E. Eg. A wound up watch spring. Derivation: Let a body of mass m be lifted from the ground to the height (h). The force required is force of gravity mg. The work done = F.S. = mgh This work is stored in the body as PE. Work done in lifting a body to a height h against gravity is called PE. Kinetic Energy: z The energy possessed by a body due to its state of motion is called its kinetic energy. KE= 1 mv2 2 Eg. A rolling stone, bullet shots from a gun. Derivation: A body of mass m is moving with a velocity v and brought to rest by a force F. Let a be the retardation produced by the force and distance travelled by the body is S. KE = Work done by the retarding force to stop it K=F S But F = ma Let initial velocity be u and final velocity, v = zero. v2 = u2 + 2as u2 = 2as 2 S= 26 [a is retardation] u [when v =0] or 2a v2 [when u = 0] 2a Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 02: Work, Energy and Power z K = ma K= 27 v2 2a 1 mv2 2 Relation between kinetic energy and momentum: z K= 1 mv2 and momentum = mv or p = mv 2 z v= p m z K= 1 1 p2 p2 m 2 = 2 2 m m or p2 = 2 K.m p= 2 K.m Work Energy Theorem: The work done by a force is equal to the increase in the kinetic energy of the body. Proof: Work done by the force = force displacement W=F S Now, v2 = u2 + 2as (i) v 2 u2 2a And F = ma From equation (i), S= v 2 u2 = 1 m (v2 u2) W = ma 2a 2 Now initial kinetic energy Final kinetic energy (ii) ki = mu2 kf = mv2 Increase in kinetic energy = kf ki = mv2 mu2 = 1 m (v2 u2) . (iii) 2 From (ii) and (iii) Work done = increase in kinetic energy W= 1 1 1 mv2 mu2 = m (v2 u2) 2 2 2 Forms of KE: The bodies in the following cases possess kinetic energy. z Translational motion (motion in a line) eg. motion of a car on a straight road. z Rotational motion (motion about an axis) eg. motion of earth around its axis. z Vibration (motion about the mean position) eg. motion of the needle of a sewing machine. Volume 1 of 2 Universal Tutorials X ICSE Physics 27 28 Law of Conservation of Energy: Energy can neither be created nor destroyed, but can be transformed from one form to another. The total energy of the universe remains constant. K + U = constant [i.e. KE + PE = constant]. Examples: i) Simple Pendulum: O z The sum of P E and K E is constant. z At A (mean position) pendulum has max. KE but PE is zero because it is at lowest position. (K.E. = mgh) z At B (extreme position) pendulum has max. PE as it has gained height but KE is zero because pendulum comes to rest. C z At C, KE = 0; PE = m.g.h (maximum) A B ii) Freely Falling Body Under Gravitational Force: z At position A. Consider a stone of mass m held at height h from the ground. z PE at A = mgh KE at A = 1 1 mv 2 = m 0 = 0 2 2 A x z TE = PE + KE = mgh z At position B: Let displacement be x and velocity be v z v2 u2 = 2as, (v2 u2 = 2gx), (v2 0 = 2gx) z z z z 1 1 mv 2 = m 2gx 2 2 KE at B = = mgx PE at B = mg (h x) = mgh mgx TE = KE + PE = mgx + mgh mgx = mgh (At position C): v2 u2 = 2gh, v2 = 2gh 1 KE = m 2gh = mgh 2 z PE at C = mgh (h h) = 0 TE = KE + PE = mgh + 0 = mgh B h h x C y mgh 1 mgh 2 Total energy KE PE h/2 A x Energy Transformations: Mechanical to Heat (Rubbing two stones/our hands together) Sound (Vibration of tuning fork/strings of musical instruments) Electrical (Generation of electricity by a dynamo) Heat to Mechanical (Heat engine) 28 Light (electric bulb) Electricity Chemical (Thermoelectric effect) (Chemical reactions) Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 02: Work, Energy and Power 29 Light to Electrical (Photo cell) Chemical (Photography) Note: Whenever mechanical energy changes to other forms it is first converted to KE and then to other forms. Power: Definition: It is the rate of doing work. P= work W = time t Unit: SI: joule / second = watt (W), C.G.S : erg / s Power is said to be 1 watt if work is done at the rate of 1 joule per second. Power is scalar quantity. Conversions: 1 Kilo watt (kW) = 1000 W 1 Watt = 107 erg s 1 1 horse power (1HP) = 746 W 1 MW = 106 W; 1GW = 109 W Expression of Power: W=F S P= W t s F S = F v (since = v) t t Work Work done by a force is equal to the product of force and the displacement in the direction of force Work done does not depend on time P= S.I unit of work is joule (J) Differences between energy and power. Energy Energy of a body is its capacity to do work. Energy spent does not depend on time. S.I. unit of energy is joule (J). Volume 1 of 2 Power Power of a source is the rate of doing work by it. Power depends on the time in which work is done. S.I unit of power is watt (W) Power Power of a source is the energy spent by it in 1s. Power spent depends on time which energy is spent. S.I. unit of power is watt (W). Universal Tutorials X ICSE Physics 29 30 Energy sources and production of Electricity: Requirements of a good Source: z A source of energy should be such that it can provide an adequate amount of useful energy at a steady rate over a longer period of time. It should be safe and convenient to use, economical and easy to store and transport. Types of sources: z Renewable sources of energy, and Non renewable sources of energy. Renewable sources These are the sources from which energy can be obtained continuously over a very long period of time. They are the non conventional sources. These are the natural sources which will never get exhausted. These sources can be regenerated. Examples: Solar energy, wind energy, hydro energy, geo thermal energy and nuclear energy Non renewable sources These are the sources from which energy can not be continuously obtained over a very long period of time. They are the conventional sources. These are the natural sources which would soon deplete. These sources can not be regenerated. Examples: Coal, petroleum and natural gas. Judicious use of energy: The conventional sources of energy i.e. fossil fuels are limited and non renewable, so the constant use of them will create an energy crisis in near future. Therefore the following measures must be taken for the judicious use of energy. z The fossil fuels such as coal, petroleum, natural gas should be used only for the limited purposes when there is no other alternative source of energy. z The wastage of energy should be avoided. z Efforts must be made to make use of energy for community or group purposes. z The cutting of trees must be banned and more and more new trees must be roped to grow. z Such a technique should be developed that in near future, we may make use of renewable sources such as solar energy, wind energy, hydro energy, geo thermal energy and nuclear energy as much as possible to meet our requirements. Production of Electricity: Solar Cell: Solar cells are usually made from semiconductors like silicon and gallium. If sunlight is made incident on an impurity added to a semiconductor, a potential difference is produced between its surfaces. This forms a solar cell. Due to this potential difference, current flows in the circuit connected between the surfaces of the semiconductor. To increase the efficiency a large number of such cells are arranged over a large area so that they collect large amount of solar energy to produce sufficient electricity. Such an arrangement of solar cells is called a solar panel. Advantages of using solar panels: z The use of solar panels for producing electricity has the following advantages: 30 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 02: Work, Energy and Power 31 They do not require any maintenance. They last over a long period of time. Their running cost is almost zero. They are most suitable for the remote, inaccessible and isolated places where electric power lines cannot be laid. They do not cause any pollution in the environment. Disadvantages of using solar panels The disadvantages of using panels are: The initial cost of solar panels is sufficiently high. The efficiency of conversion of solar energy to electricity is low. A solar panel produces direct current which cannot be directly used for household purposes. z d.c. cannot be stepped up or down as required. z z z z Solar power plant A solar power plant is a device in which heat energy of sun is used to generate electricity. A solar power plant consists of a number of concave reflectors, at the focus of which there are black painted water pipes. Water inside the pipes starts boiling and produces steam. The steam thus produced is used to rotate a steam turbine which drives a generator producing electricity. Wind energy: Wind energy is used in a wind generator to produce electricity by making use of a windmill (or wind turbine) to drive a wind generator. The electric power generated by a single wind generator is very small. So to generate a large amount of electric power, a large number of such wind generators are arranged over a big area called a wind farm, and then the electric power generated by each generator is combined together for supply to the consumers. Advantages and limitations: z The use of wind energy for generating electricity has the advantage that it does not cause any kind of pollution and it is a long lasting (i.e. renewable) source. z The limitations of use of wind energy for electric power generator are: z The wind farms can be established only at places where wind blows around the year steadily with a minimum speed of 15 km h 1, z A large area of land is needed for the establishment of a wind farm and z Establishing a wind farm is expensive. z Wind mills need regular maintenance which is expensive and recurring. Hydro Electricity: The kinetic energy possessed by flowing water is called the water (or hydro) energy. The water flowing in high altitude rivers is collected in a high dam (or reservoir). The water from dam is then allowed to fall on a water turbine which is located near the bottom of the dam. The shaft of the turbine is connected to the armature of an electric generator (or dynamo) As the turbine rotates, it runs the generator, to produce electricity. Volume 1 of 2 Universal Tutorials X ICSE Physics 31 32 Advantages and limitations (or disadvantages): z The advantages of using hydro energy for generation of electricity are it does not produce any environmental pollution. the dams constructed over rivers help us in irrigation and they control floods. z The limitations of using hydro energy for producing electricity are: the flowing water is not available every where due to the construction of dams over the rivers, plants and animals of that place get destroyed or killed and the ecological balance in the downstream areas of rivers gets disturbed. the rehabilitation of people and animals will be neccessited. Nuclear Energy: When a heavy nucleus is bombarded with slow neutrons, it splits into two nearly equal light nuclei with release of tremendous amount of energy. in the form of heat. This process is called nuclear fission. When two or more light nuclei combine at a very high pressure and high temperature to form a heavy nucleus with a release of tremendous amount of energy, as heat the process is called nuclear fusion. Both in nuclear fission and nuclear fusion, the total sum of masses of products is less than the total sum of masses of reactants. [This lost mass gets converted into energy, according to the Einstein s mass energy relation, E = mc2 where c is the speed of light (= 3 108 m s 1), m is the loss in mass and E is the energy released]. The energy so released is called the nuclear energy. Heat energy released due to the controlled chain reaction of nuclear fission of uranium 235 (or plutonium 239) in a nuclear reactor is absorbed by the coolent. The water in heat exchanger gets heated and converts into steam. The steam is used to rotate the turbine which in turn rotates the armature of generator in a magnetic field and thus produces electricity. Advantages and limitations: There are two main advantages of using nuclear energy for the production of electricity z A very small amount of nuclear fuel (such as uranium 235) can produce a tremendous amount of energy, for a long time. z Once the nuclear fuel is loaded into a nuclear power plant, it continues to release energy for several years. The main limitation is that it is not a clean source of energy because very harmful nuclear radiations are released in the process which is highly energetic and penetrating. [They cause ionization and so they are very harmful to the human body, so it needs a high standard of protection for the persons working with the power plant and also for the environment]. The nuclear fusion is preferred over the fission as an energy source because the fuel needed for fusion is hydrogen or isotope of hydrogen which is available in abundance, and the fusion reaction does not produce any harmful products. But fusion is not viable under lab conditions. 32 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 02: Work, Energy and Power 33 TYPICAL SOLVED EXERCISES: 1) A girl of mass 50 kg climbs a flight of 100 stairs each measuring 0.25 m in height in 20 sec. Find a) force acting on the girl b) work done by the girl c) gain in PE d) Power in (i) Watt (ii) Horse power (g = 10 ms 2) Ans: m = 50 kg; h = 0.25 100 m; t = 20 s. a) F = mg = 50 kg 10 m s 2 = 500 N b) W = F.d = 500 N 25 m = 12500 J c) PE = Total work = 12500 J 625 W 12500 d) (i) P = ii) 1 HP = 746 W = 0.8378 H.P. = = 625 W 746 t 20 2) An electric pump is 60% efficient and is rated 2 H.P. Calculate the maximum amount of water it can lift through a height of 5m in 40 sec. (g = 10 ms 2) 60 Ans: 2 H.P = 2 746 W 60% = 2 746 = 895.2 W 100 W W h = 5m t = 40sec P= 895.2 = t 40 m g h 895.2 40 mg = mg = 7161.6 kg 5 40 7161 .6 m= = 716 .6 kg 10 A body has a mass of 5 kg and velocity 5 ms 1. Find K.E. Find the ratio of initial K.E. and final K.E., if it s a) mass is tripled, b) velocity is made four times. 1 1 Initial K.E. = mv 2 = 5kg (5ms 1 )2 = 62.5 J 2 2 1 1 a) Final K.E = mv 2 = 15kg (5ms 1 )2 = 187.5 J 2 2 Ratio of initial and final K.E. = 62.5 J: 187.5 J = 1:3 1 1 b) K.E. = mv 2 = 5kg (20ms 1 )2 = 1000 J. 2 2 Ratio of initial and final K.E. = 62.5 J : 1000 J = 1:16 A bullet of mass 10 g strikes a wooden target 10 cm thick with a velocity of 400 ms 1 and emerges out with a velocity of 100 ms 1. Find i) Initial K.E. ii) Final K.E. iii) Loss of K.E. in overcoming friction iv) Average force of friction of wood. Mass of bullet = 10 gm = 0.01 kg 1 1 i) Initial kinetic energy = mv 2 = 0.01kg ( 400 ms 1 )2 = 800 J 2 2 1 ii) Final kinetic energy = 0.01kg (100 ms 1 )2 = 50 J 2 iii) Loss of K.E. = (800 50) J = 750 J Work done in penetrating through wood=750J 10 iv) Also work done in penetrating through wood = F distance = F m 100 10 F F = 7500 N m = 750 J . Hence, 100 895.2 = 3) Ans: 4) Ans: Volume 1 of 2 Universal Tutorials X ICSE Physics 33 34 REVIEW QUESTIONS: Direct questions: 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) Define work. Is work a scalar or a vector? A body is acted upon by a force. State two conditions when the work done is zero What do you mean by degradation of energy? Explain it by taking two examples of your daily life. The work done by a fielder when he takes a catch in a cricket match is negative. Explain. What are the S.I. and C.G.S units of work? How are they related? Establish the relationship. State and define the S.I. unit of work. Express joule in terms of erg. Define the term energy and state its S.I unit Define the term power. State its S.I. unit. Differentiate between work and power. State and define the S.I unit of power. Write the S.I and C.G.S. units of power. How are they related? Define a kilowatt hour. How is it related to joule? What are the two forms of mechanical energy? Name the form of energy which a wound up watch spring possesses. Define the term potential energy of a body. How is it measured? Write an expression for the potential energy of a body of mass m placed at a height h above the earth s surface. What do you understand by the term kinetic energy of a body? Differentiate between potential energy (U) and kinetic energy (K). Energy can exist in several forms and may change from one form to another. For each of the following, state the energy changes that occur in: a) the unwinding of a watch spring, b) a loaded truck when started and set in motion c) a car going uphill d) photosynthesis in green leaves e) charging of a battery f) respiration g) burning of a match stick h) explosion of crackers What is meant by renewable and non-renewable sources of energy? Distinguish between them, giving two examples of each. State advantages and disadvantages of producing electricity from solar energy. State two advantages and two disadvantages of using wind energy for generating electricity. State two advantages and two disadvantages of producing hydroelectricity. What percentage of total electrical power generated in India is obtained from nuclear power plants? Name two places in India where electricity is generated from nuclear power plants. State four ways for the judicious use of energy. State the law of conservation of energy. State the condition when the work done by a force is (i) positive, (ii) negative. Explain with the help of examples NUMERICALS: Class Work: 1) A body, when acted upon by a force of 10 kgf gets displaced by 0.5m. Calculate the work done by the force, when the displacement is (i) in the direction of force, (ii) at an angle of 60 with the [50 J, 25J, zero] force, and (iii) normal to the force (g = 10N kg 1) 2) It takes 20 s for a person A to climb up the stairs, while another person B does the same in 15 s. Compare the (i) work done and (ii) power developed by the persons A and B. [1:1, 3:4] 34 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 02: 0 Work, Ene ergy and Pow wer 35 3) A man spends s 6.4 kJ energy in displa acing a body y by 64 m in the direction in which he h applies for rce, in 2.5 s. Calculate: i) ) the force ap pplied and (ii) the power spent s (in H.P P) by the man. [100N, 3.43 3 H.P] 4) A machine rais ses a load of f 750 N throu ugh a height of 16 m in 5 s. Calculate. 100N, 3.43 3 H.P (i) energy spen nt by machin ne (ii) power at a which the machine wo orks [( (i) 12000J, ii) ) 2400W] 5) A boy of mass s 40 kg runs s up a flight of o 15 steps each e 15 cm high in 10 s s. Find the work w done an nd the power r developed by b him. Take e g = 10 N kg g 1 [900 J, 90 W] 6) A man raises a box of 50 kg k mass to a height of 2 m in 2 minu utes, while an nother man raises r the sa ame box to the same height in 5 minutes. m Com mpare: (i) th he work don ne and (ii) th he power [1:1, 5:2] de eveloped by them. t 7) An n ox can app ply a maximum force of 1000 N. It is taking t part in n a cart race and is able to t pull the ca art at a const tant speed of 30 m s 1 while w making its best effor rt. Calculate the power developed d by y the ox. [30kwh] 8) A box of weigh ht 150 kgf ha as gravitation nal potential energy store ed in it equal l to 14700 J. Taking g 98 [10 m] 8 N kg 1, find the height of o the box above the grou und. 9) Ca alculate the height h throug gh which a body b of mass s 0.5 kg should be lifted if the energy y spent in [0.2 m] do oing so is 1.0 0 J. Take g = 10 m s 2 10) A vessel conta aining 50 kg of water is placed at a height 15 m above the g ground. Assu uming the gra avitational po otential ener rgy at ground d to be zero, what will be e the gravitat tional potential energy [7500 J] of water in the vessel? (g = 10 m s 2) 11) A block A, who ose weight is s 200 N, is pulled up a slope of length h5m by y means of a constant for rce F (= 150 N) as illustra ated in Fig. 2.12. 2 a) What is the work done by b the force F in moving the block A, A 5m alo ong the slope e? b) By how muc ch has the po otential energy of the blo ock A increas sed? c) Account for r the differen nce in work done d by the force and th he increase in potential energy e of the e block. [(i) 750 J (ii) 600 J( iii) Used agains st friction] 12) A cannon ball l of mass 50 00 g is fired d with a spe eed of 15 m s 1. Find it ts kinetic en nergy and mo omentum. [56.25J, 7.5kgms 1] 13) A body of mas ss 10 kg is moving m with a velocity 20 m/s. m If the mass m of the bo ody is double ed and its ve elocity is halv ved, find the ratio of the in nitial kinetic energy e to the e final kinetic c energy. 14) A body of mas ss 60 kg has the moment tum 3000 kg m s 1. Calcu ulate the kine etic energy and a speed [7.5 104J, 50ms 1] of the body. ow much ene ergy is gaine ed by a box of o mass 20 kg g when 15) Ho a) a man carry ying the box waits w for 5 minutes m for a bus? rying the box x with a spee ed of 3 m s 1 catch the bu us? b) he runs carr [zero, 90 c) he raises it by b 0.5 m in order o to place e it inside the e bus? (g = 10 1 m s 2) 0J, 100 J] 1 16) A stone of mas ss 500 g is thrown vertic cally upwards s with a velocity of 15 m s . Calculat te: (a) the po otential energ gy at the grea atest height, (b) the kinet tic energy on n reaching th he ground, (c c) the total en nergy at its ha alf way point t. [ 56.2 25 J, 56.25 J, J 56.25J] 17) Th he diagram given g below shows a ski jump A skier weighing 60 kgf sta ands at A at the top of sk ki jump. He moves m from A to B and ta akes off for r his jump at B a) Calculate th he change in i the gravitational potential energy of the sk kier between A and B. b) If 75% of the energy in part p (a) beco omes kinetic energy at B, calculate th he speed at which w the sk kier arrives at t B. (Take g = 10 m s 2) [3.6 104J 30ms 1] 18) Th he bob of a simple s pendu ulum is impa arted a veloc city 5 m s 1 when w it is at its mean po osition. To wh hat maximum m vertical hei ight will it rise e on reaching to its extre eme position if 60% of its energy is 2 [0.5 m/s] los st in overcom ming friction of o air? Take g = 10 m s 2 ? Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 35 36 Home Work: 1) A boy of mass 40 kg runs upstairs and reaches the 8 m high first floor in 5s. Calculate: i) the force of gravity acting on the boy. ii) the work done by him against gravity. [400 N, 3200J] 2) A boy weighing 350 N runs up a flight of 30 steps, each 20 cm high in 1 minute. Calculate the work done and power spent. [2100 J, 35 W] 3) A weight lifter lifted a load of 200 kgf to a height of 2.5 m in 5 s. Calculate: (i) the work done, and [5000 J, 1000 W] (ii) the power developed by him. Take g = 10N kg 1 4) An electric heater of power 3 kW is used for 10 h. How much energy does it consume? [30kw] 5) A water pump raises 50 litres of water through a height of 25 m in 5 s. Calculate the power which [2500 W] the pump supplies (Take g = 10N kg 1 density of water = 1000 kg m 3) 6) A pump is used to lift 500 kg of water from a depth of 80 m in 10s. Calculate: a) the work done by the pump, b) the power at which the pump works, 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 36 c) the power rating of the pump if its efficiency is 40% (Take g = 10 ms 2) [4 105J,40kw, 100kw] If the power of a motor is 40 kW, at what speed can it raise a load of 20, 000 N? [2 ms 1] Find the gravitational potential energy of 1 kg mass kept at a height of 5 m above the ground if g [50 J] 10 m s 2 A body of mass 5 kg falls from a height of 10 m. How much energy does it possess at any [500 J] instant? (Take g = 10 m s 2). A boy weighing 25 kgf climbs up from the first floor at height 3 m above the ground to the third floor at height 9 m above the ground. What will be the increase in his gravitational potential [1500 J] energy? (Take g = 10 N kg 1) Calculate the work done by a man of mass 50 kg when he climbs up a ladder of height 10 m. [4900 J, 4900J] Also calculate the increase in his potential energy. (g = 98 m s 2). Find the kinetic energy of a body of mass 1 kg moving with a uniform velocity of 10 m s 1. [50 J] A ball of mass 0.5 kg slows down from a speed of 5 m s 1 to that of 3 m s 1. Calculate the change in kinetic energy of the ball. [4J] A bullet of mass 50 g is moving with a velocity of 500 m/s. It penetrates 10 cm into a still target and comes to rest. Calculate. a) the kinetic energy possessed by the bullet, b) the average retarding force offered by the target. [6250 J, 62500 N] 1 1 A truck weighing 1000 kgf changes its speed from 36 km h to 72 km h in 2 minutes. Calculate [1.5 105J, 1.25 103W] (i) the work done by the engine and (ii) its power. (g = 10 m s 2) How much work is needed to be done on a ball of mass 50 g to give it a momentum of [2.5 10 4 J] 500 g cms 1? A ball of mass 0.20 kg is thrown vertically upwards with an initial velocity of 20 m s 1. Calculate the maximum potential energy it gains as it goes up. [40 J] A hydroelectric power station takes its water from a lake whose water level is 50 m above the turbine. Assuming an overall efficiency of 40%, calculate the mass of water which must flow [5000 g] through the turbine each second to produce power output of 1MW. (g = 10 m s 2) A metal ball of mass 2 kg is allowed to fall freely from rest from a height of 5 m above the ground (Take g = 10 m s 2) a) Calculate the potential energy possessed by the ball when initially at rest b) What is the kinetic energy of the ball just before it hits the ground? c) What happens to the mechanical energy after the ball hits the ground and comes to rest? [100J, 100J, converts to heat and sound] Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 02: Work, Energy and Power 37 APPLICATION TYPE: Class Work: 1) How is the work done by a force measured when (i) force is the direction of displacement (ii) force is at an angle to the direction of displacement? 2) A boy of mass m climbs up a staircase of vertical height h. What is the work done by the boy against the force of gravity? What would have been the work done if he uses a lift in climbing the same vertical height? 3) Name the physical quantity which is measured in calorie. How is it related to the S.I unit of that quantity? 4) When an arrow is shot from a bow, it has kinetic energy in it. Explain briefly from where does it get its kinetic energy? 5) A body of mass m is moving with a velocity . Write the expression for its kinetic energy. 6) A body of mass m is moving with a uniform velocity u. A force is applied on the body due to which its velocity changes to v. How much work is being done by the force? 7) Is it possible that no transfer of energy may take place even when a force is applied to a body? 8) A body falls freely under gravity from rest. Name the kind of energy it will possess at the point from where it falls, (b) while falling (c) on reaching the ground. 9) Show that the sum of kinetic energy and potential energy (i.e. total mechanical energy) is always conserved in the case of a freely falling body under a gravity (with air resistance neglected) from a height h by finding it when (i) the body is at top, (ii) the body has fallen a distance x, (iii) the body has reached the ground. 10) Two bodies of equal masses are placed at heights h and 2h. Find the ratio of their gravitational potential energies. 11) Two bodies of equal masses are moving with uniform velocities v and 2v. Find the ratio of their kinetic energies. 12) What is the work done against gravity when a body is moved horizontally along a frictionless surface? 13) Give examples of bodies possessing both PE and KE at the same time 14) A man rowing a boat upstream is at rest with respect to the shore. Is he doing any work? If he stops rowing and moves down with the stream, is any work being done on him? 15) What is the work done in holding a 5 kg suitcase while waiting for a train for 10 minutes? Give reason for your answer. 16) When a porter carrying a suitcase in his hand or on his head is walking horizontally, the work done against gravity is zero . Is the statement true? If Yes then explain why the statement is true. 17) A light mass and a heavy mass have equal momentum. Which will have more KE? Explain. 18) What is the relation between KE, momentum and mass? Derive it. 19) State the energy changes which take place in the following cases: i) A bulb glows when torch light is switched on. ii) A toy car is wound and then allowed to move on the floor. iii) A car moves up a hill. iv) Water in the dams, rotates the turbines of dynamo. v) An air gun is loaded and then fired. vi) A piece of magnesium burns in air. vii) Water freezes in the freezing chamber of a fridge. viii) A stone is dropped from a cliff. ix) Food is eaten by human beings. x) Photographic film is exposed to sun light. Volume 1 of 2 Universal Tutorials X ICSE Physics 37 38 20) A block of mass 30 kg is pulled up a slope with a constant B speed by applying a force of 200 N parallel to the slope. A and B are initial and final positions of the block. 1.5m 3m i) Calculate work done by the force in moving the block from A to B. 200N A ii) P.E. of the block. 21) A block B, whose weight is 200 N, is pulled up a slope at a constant speed by means of a constant force A (150 N), as illustrated in Fig. a) What is the work done by the force A in moving the block B, 5 m along the slope? 3m 5m B b) By how much has the potential energy of the block B increased? Force A c) Account for the difference. Home Work: 22) When a body moves in a circular path, how much work is done by the body? Give reason 23) What physical quantity does the electron volt (eV) measure? How is it related to the S.I unit of that quantity? 24) What is horse power (H.P.)? How is it related to the S.I unit of power? 25) Name the form of energy which a body may possess even when it is not in motion. Give an example to support your answer. 26) State the work-energy theorem. 27) A light mass and a heavy mass have equal momentum. Which will have more kinetic energy? 28) In what way does the temperature of water at the bottom of a waterfall differ from the temperature at the top? Explain the reason. 29) A body is thrown vertically upwards. Its velocity keeps on decreasing. What happens to its kinetic energy as its velocity becomes zero? 30) Explain the energy changes in an oscillating simple pendulum. How does the mechanical energy remain constant in it? 31) If the speed of a car is halved, by which factor does its kinetic energy change? 32) A car is running at a speed of 15 km h 1 while another similar car is moving at a speed of 30 km h 1. Find the ratio of their kinetic energies. 33) What should be the angle between the direction of force and the direction of motion of a body so that the work done is zero? 34) In a tug of war, team A is slowly giving way to team B. What work is being done, and by whom? 35) Does work done in raising a box onto a platform depend on how fast it is raised? 36) From the ground floor, a man comes up to the fourth floor of a building, using the staircase. Another person comes up to the same floor using an elevator. Neglecting friction, compare the work done in the two cases. 37) A string, suspended from a fixed point, has a small mass swinging to and fro at the other end. With respect to the string, state whether the following statements are true or false. i) The PE is the maximum in the centre position of the swing. ii) The KE is the maximum in the centre position of the swing iii) The sum of PE and KE is constant throughout the swing. iv) The number of swing decreases with time. 38) i) In what case is the PE equal to zero? ii) In what case is the KE assured to the zero? 39) In which of the cases work is done and why? i) A man pushing a wall. 38 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 02: Work, Energy and Power 39 ii) A girl climbing a stair case. iii) A boy swimming in a tank. iv) A man standing at a place and holding a suitcase in his hand. v) A lady cooking food. vi) A porter carrying a heavy load on his head and walking along a level road. 40) Give one example in each case: i) When heat energy changes to kinetic energy. ii) When kinetic energy changes to heat energy. iii) When sound energy changes to electric energy. iv) When electric energy changes to sound energy. v) When light energy changes to chemical energy. vi) When chemical energy changes to light energy vii) When electric energy changes to magnetic energy. viii) When magnetic energy changes to electric energy. ix) When potential energy changes to electric energy. x) When electric energy changes to potential energy. 41) A truck driver loads some oil drums into a truck by lifting them directly. Each drum has mass 80 kg and the platform of the truck is 0.8 m above the ground. i) How much force is needed to lift the drum into the truck? ii) How much energy is used up in lifting the drum? iii) After the truck is loaded, the driver drives off. List the major energy changes that take place in moving the truck. iv) The driver stops the truck at the factory gate. What happens to the K.E. of the truck? 42) A girl sits and stands repeatedly for 5 minutes. Draw a graph to show the variation of PE with time. MISCELLANEOUS: 1) A force F acts on a body and displaces it by a distance S in a direction at an angle with the direction of force. Write the expression for the work done by the force. What should be the angle between the force and displacement to get the (i) minimum work, (ii) maximum work? 2) The work done by a force on a body will be positive if the: a) body does not move b) body moves perpendicular to the direction of the applied force c) body moves along the direction of the applied force d) body moves opposite to the direction of the applied force. 3) A satellite revolves around the earth in a circular orbit. What is the work done by the force of gravity? 4) In which of the following cases, is work being done? i) A man pushing a wall ii) A coolie standing with a load of 12 kgf on his head. iii) A boy climbing up a staircase. iv) A boy carrying a box on his head and moving on a frictionless horizontal surface. 5) Give an example when work done by the force of gravity acting on a body is zero even though the body gets displaced from its initial position. 6) One joule work is said to be done when: a) a force of 1 N displaces a body by 1 cm b) a force of 1 N displaces a body by 1 m c) a force of 1 dyne displaces a body by 1 cm d) a force of 1 dyne displaces a body by 1 m 7) Complete the following sentence: 1 J = .. calorie. Volume 1 of 2 Universal Tutorials X ICSE Physics 39 40 8) Kilowatt is the unit of: a) work b) momentum c) force d) power 9) One horse power is equal to: a) 1000 W b) 500 W c) 764 W d) 746 W 10) Complete the following sentences: a) The S.I unit of work is _______ of energy is _______ and of power is b) kilowatt is the unit of _______ and kWh is the unit of _______ c) joule is the unit of ___________ d) 1 J = ____________.erg e) 1 H.P = _____________ W f) 1 eV =_______________J g) 1 kWh = ____________J 11) What are the different forms of energy? Name them. 12) Name the type of energy (kinetic energy K or potential energy U) possessed in the following cases: a) A moving cricket ball b) A compressed spring c) A moving bus d) The bob of a simple pendulum at its extreme position. e) The bob of a simple pendulum at its mean position. f) A piece of stone placed at the roof. 13) Name the two forms of potential energy and give one example of each. 14) What is meant by the gravitational potential energy? 15) Name the three forms of kinetic energy and give one example of each. 16) Complete the following sentences a) The kinetic energy of a body is the energy by virtue of its _________ b) The potential energy of a body is the energy by virtue of its __________ 17) Name the form of mechanical energy, which is put to use. 18) State the energy changes in the following cases while in use a) loudspeaker b) a steam engine c) microphone d) washing machine e) an electric bulb f) burning coal g) a solar cell h) bio-gas burner i) an electric cell in a circuit j) a petrol engine of a running car k) an electric toaster l) a photovoltaic cell m) an electromagnet. 19) What should be the characteristic of a source of energy? Name the two groups in which various sources of energy are classified. 20) Select the renewable and non-renewable sources of energy from the following: (i) Coal, (ii) Wood, (iii) Water, (iv) Diesel, (v) Wind. 21) Why is the use of wood as a fuel not advisable although wood is a renewable source of energy? 22) What is the main source of energy for the earth? 23) What is solar energy? How is the solar energy used to generate electricity in a solar power plant 24) What is a solar cell? How do you use solar cell to obtain electricity from the solar energy? State two uses of solar cells. State whether a solar cell produces a.c. or d.c. 25) What is wind energy? How is wind energy used to produce electricity? How much electric power is generated in India using the wind energy? 26) What is hydro energy? Explain the principle of generating electricity from hydro energy. How much hydro electric power is generated in India? 27) What is nuclear energy? Explain the principle of producing electricity using the nuclear energy. 40 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 02: Work, Energy and Power 41 28) State two advantages and two disadvantages of using nuclear energy for producing electricity. 29) State the energy transformation in the following: i) electricity is obtained from solar energy. ii) electricity is obtained from wind energy. iii) electricity is obtained from hydro energy. iv) electricity is obtained from nuclear energy. 30) What do you understand by the conservation of mechanical energy? 31) Name two examples in which the mechanical energy of a system remains constant. 32) A pendulum is oscillating on either side of its rest position. The correct statement is: a) It has only the kinetic energy. b) It has the maximum kinetic energy at its extreme position c) It has the maximum potential energy at its rest position. d) The sum of its kinetic and potential energies remains constant throughout the motion. 33) Express giga joule (GJ) and giga watt in their SI units. 34) What is the measure of the potential energy of a body at a certain height above the surface of the Earth? 35) A man climbs a slope and another man walks same distance on a level road. Who does more work and why? 36) Show that power is a product of force and velocity. 37) What kind of energy is possessed by a body in the following cases? i) A cocked up spring of an air gun ii) A shooting arrow iii) A stone lying on the top of house iv) Water stored in dams v) Fish moving in water vi) An electron spinning around a nucleus. vii) A running car along a level road. PREVIOUS BOARD QUESTIONS: 1) A ball is placed on a compressed spring. When the spring is released, the ball is observed to fly away. i) What form of energy does the compressed spring possess ? ii) Why does the ball fly away? [2012] 2) i) State the energy conversion taking place in a solar cell. ii) Give one disadvantage of using a solar cell. [2012,] 3) A body of mass 0.2 kg falls from a height of 10 m to a height of 6 m above the ground. Find the loss in potential energy taking place in the body. (g = 10 m s 2) [2012, 8 J] 4) A moving body weighing 400 N possesses 500 J of kinetic energy. Calculate the velocity with [2012, 5 ms 1] which the body is moving (g = 10 m s2). 5) A ball of mass 200 g falls from a height of 5 cm. What will be its kinetic energy when it just [2011, 0.098 J] reaches the ground? [g = 9.8 ms 2] 6) What is meant by Energy degradation? [2011] 7) Draw a diagram to show the energy changes in an oscillating simple pendulum. Indicate in your diagram how the total mechanical energy in it remains constant during the oscillation. [2011] 8) What is the S I unit of energy? How is the electron volt (ev) related to it? [2009] 9) A body of mass 5 kg is moving with a velocity of 10 m/s. What will be the ratio of its initial kinetic energy and final kinetic energy, if the mass of the body is doubled and its velocity is halved? [2009, 2:1] A 10) An object of mass m is allowed to fall freely from point A as shown in figure. x Calculate the total mechanical energy of the object at: B i) Point A y ii) Point B C iii) Point C iv) State the law which is verified by your calculations in part (i), (ii), and (iii). [2009] Volume 1 of 2 Universal Tutorials X ICSE Physics 41 42 11) When an arrow is shot from a bow, it has kinetic energy in it. Explain briefly from where does it get its kinetic energy? [2008] 12) A stone of mass 64.0 g is thrown vertically upward from the ground with an initial speed of 20.0 m/s. the gravitational potential energy at the grounded level is considered to be zero. Apply the principle of conservation of energy and calculate the potential energy at the maximum height attained by the stone. [2008, 12.83] 13) Define joule , the S unit of work and establish a relationship between the S and CGS unit of work. [2008] 14) Two bodies, A and B of equal mass are kept at heights 20 m and 30 m respectively. Calculate the ratio of their potential energies [2007. 2:3] 15) Define a kilowatt hour. How is it related to the joule? [2007] 16) How can the work done be measured when force is applied at an angle to the direction of displacement? [2007] 17) What is the main energy transformation that occurs in: [2007] i) Photosynthesis in green leaves? ii) Charging of a battery? 18) Mention any two differences between the mass and weight of a body [2006] 19) State the amount of work done by an object when it moves in a circular path for one complete rotation. Give a reason to justify your answer [2006] 20) Calculate the height through which a body of mass 0.5 kg should be lifted if the energy spent for doing so is 1.0 joule (g = 10 ms 2). [0.2 m] 21) a) Which physical quantity does the electron volt measure? How is it related to the S.I unit of this quantity? b) What should the angle between force and displacement be to get: i) minimum work ii) maximum work. c) The work done by the heart is 1 joule per beat. Calculate the power of the heart, if it beats 72 times in one minute. [2005, 1.2 W] 22) i) State the law of conservation of energy. ii) Name the chief energy transformation that occurs. In a Loudspeaker; In an Electrical cell (Primary). [2005] 23) i) State the energy changes in an oscillating pendulum. ii) Two balls of mass ratio 1:2 are dropped from the same height. State the ratio between their velocities when they strike the ground. The ratio of the forces acting on them during motion. [2004, 1:2] 24) A ball of mass 0.20 kg is thrown vertically upwards with an initial velocity of 20m/s. Calculate the maximum potential energy it gains as it goes up. [2004, 40 J] 25) i) The weights of two bodies are 2.0N and 2.0 kgf respectively. What is the mass of each body? (g = 10 ms 2) ii) If the power of a motor is 40 kW, at what speed can it raise a load of 20,000 N? [2003, 0.2 kg, 2kg] 26) i) A machine raises a load of 750 N through a height of 16m in 5 seconds. Calculate the power at which the machine works. ii) State the principle of conservation of energy. [2002, 2400 W] 27) a) Define: (i) Work (ii) Power and (iii) Energy b) How is work done related to the applied force? c) By what factor does the kinetic energy of a moving body change when its speed is reduced to half? d) From the ground floor, a man comes up to the fourth floor of a building using the stair case. Another person comes up to the same floor using an elevator. Neglecting friction, compare the work done in the two cases. [2002] 42 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 02: Work, Energy and Power 43 28) A truck driver starts off with his loaded truck. What are the major energy changes that take place in setting the truck into motion? [2001] 29) A body P has a mass of 20 kg and is moving with a velocity of 5 m/s. Another body Q has a mass of 5 kg and is moving with a velocity of 20 m/s. Calculate the ratio of momentum of body P to body Q. Calculate the kinetic energy of P in S.I. units. [2000, 1:1, 250J] 30) State the transformation of energy which takes place in the following when current is drawn from them: (i) An electric cell (ii) A generator. [1999] 31) A machine is driven by a 100 kg mass that falls 8.0 m in 4.0 s. It lifts a load of mass 500 kg vertically upwards. [1999] i) What is the force in newton, exerted by the falling mass? [1000] ii) What is the work done by 100 kg mass falling through 8.0m? [8000 J] iii) What is the power input to the machine? [2000 W] iv) If efficiency of the machine is 75% or 0.75, what is the power output of the machine? [1500W] [600 J] v) What is the work done by the machine in 4.0 s? (Take g = 10 m/s2). 32) i) What is the S.I. unit of work? ii) A body of mass 1 kg falls from a height of 5 m. How much energy does it possess at any [49 J] instant, (take g = 9.8 m/s2)? iii) When a body moves in a circular path how much work does it do? [1998, 0] 33) A bullet of mass 50 g is moving with a velocity of 500 m/s. It penetrates 10cm into still target and comes to rest. i) Calculate the kinetic energy possessed by the bullet. [6,250 J] ii) The average retarding force offered by the target. [1998, 62500N] 34) i) How fast should a man weighing 60kg, run so that his kinetic energy is 750 J? [1997] 1 ii) A body of mass 1kg is thrown vertically up with an initial speed of 5ms . What is the magnitude and direction of force due to gravity acting on the body when it is at its highest point? [5 m/s, 9.8 N] 35) A block of mass 30kg is pulled up a slope (diagram alongside) with a constant speed by applying a force of 200 N parallel to the slope. A B and B are initial and final positions of the block. i) Calculate the work done by the force in moving the block from A to B. [150J] 1.5m 3m 200 ii) Calculate the potential energy of the block. [1997, 450J] A C 36) State the energy changes which take place while using the following: [1996] i) A microphone ii) an electric bulb and iii) A steam engine 37) a) A man of mass 60kg runs up a flight of 30 steps in 15 seconds. If each step is of 20 cm high, calculate the power developed by the man. Take g = 10 ms 2. b) i) Define work and its S.I. unit. ii) Write an expression for the work done by constant force acting on a body that gets displaced from its initial position in a direction different from the direction of the force. iii) Give an example when work done by force acting on a body is zero even through the body gets displaced from its initial position by the application of the force. [1996, 240W] ANSWERS: Previous Board Question: 1) i) The compressed spring possesses the elastic potential energy. ii) When the spring is released, the potential energy of spring changes into its kinetic energy which does work on the ball placed on it and makes the ball fly away. Volume 1 of 2 Universal Tutorials X ICSE Physics 43 44 2) i) In a solar cell, the light energy changes to the electrical energy. ii) The efficiency of conversion of light energy into the electrical energy is very low. 3) Given m = 0.2 kg, g = 10 m s 2, h1 = 10 m, h2 = 6 m Loss in potential energy = m g(h1 h2) = 0.2 10 (10 6) = 8 J 4) Given: W = 400 N, g = (10 ms 2), K.E. = 500 J, v = ? Mass, m = 500 = 400 N 1 mv2 = 40 kg, K.E. = 2 10 ms 2 2 500 = 40 1 40 v2 or v = 2 25 = 5 ms 1 5) 0.098J 8) SI unit of energy is joule; 1 ev = 1.6 10 19 J. 9) m = 5 kg; u = 10 m/s Final, K.E. = Initial K.E. = 1 1 12 m (u ) 2 So Final, K.E = 1 1 mu2 = 5 (10)2 = 250 J 2 2 [Here, m1 = 10 kg; U1 = 5 m/s] Initial K.E 250 2 1 = = 10 (5)2 = 125 J Final K.E 125 1 2 10) i) Point A, PE = mg (x + y); K.E. = 0 Total mechanical energy E = PE + K.E. E = mg (x + y) ii) Point B, PE = mgy K.E. = 1 2 mvB 2 As, v2 = u2 + 2gx; vB2 = 2gx So, K.E. = 1 m 2gx 2 K.E. = mgx; E = P.E + K.E. E = mg (x + y) iii) Point C, PE = 0 KE = 1 2 mv C 2 1 m 2g (x + y) K.E. = mg (x + y) 2 E = P.E. + K.E. E = P.E + K.E. E = 0 + mg (x + y) E = mg (x + y) iv) Law of conservation of energy: Energy can neither be created nor destroyed. Only one from of energy changes into another form and total energy is conserved. 12) 12.8 J 14) 2:3 19) Zero because w = FS cos and cos 90 = 0 As v2 = u2 = 2ac 2 vC = 2g (x + y); So, K.E = 1 = 0.2 m 0.5 10 Energy: The electron volt is related to the S.I. unit of energy (joule) by the relation: 1eV = 1.6 10 19J. Work done by the force W = F cos S, where is the angle between direction of force and displacement of body. If is 90 , then W = F cos 90 S = 0, i.e., work done is minimum. If = 0, then W = F cos 0 S = F S, i.e., work done is maximum. Total work done by the heart in one minute (i.e. 60 s) is 72 beats or 72 joules. 20) 1 = mgh; h = 21) a) b) i) ii) c) Power of the heart = 44 W (in joules) 72 = watt = 1.2 watt. time (in s) 60 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 02: Work, Energy and Power 45 22) The law of conservation of energy states that the energy can neither be created, nor be destroyed. It can only be transformed from one another form such that the total energy of the system remains constant. In a loudspeaker: Electric energy changes into sound energy. In a primary cell: Chemical energy changes into electric energy. 23) i) In an oscillating pendulum, kinetic energy and potential energy keep changing with position. At mean position and extreme position, the K.E. and P.E. are maximum respectively. ii) 1 : 1 as velocity is independent of mass. Ratio of forces: f1 m1g = f2 m2g f1 m1 1 = = f2 m 2 2 Ratio is 1 : 2 1 1 mv 2 = 0.2 20 20 = 40 J. 2 2 According to conservation of energy, Max. P.E. = Max. K.E. = 40 J. 25) i) Weight of body = 2N 24) Maximum kinetic energy = 2 = m1 10; W1 = m1g m1 = 2 = 0.2 kg 10 Weight of body = 2.0 kgf 20 = 2 kg. 10 W2 = m2g as 2kgf = 2 10 N 2 10 = m2 10 Power = 40 kW = 40,000 W F = 20,000 N Power = Force Average speed 40,000 = 20,000 Average speed Average speed = m2 = 40,000 = 2 m/s 20,000 Work F d 750 16 = = = 2400 watt. t 5 Time The principle of conservation of energy states that energy can neither be created nor destroyed. It can only be transformed from one form to another. The total energy of the system remains constant. Work is said to be done when a force applied on a body displaces it in the same direction. It is equal to the product of force and displacement. Power is defined as rate of doing work. Energy is defined as capacity or ability to do work. Work is said to be done only when applied force displaces the body in the same direction, Work is directly proportional to force. 26) i) Power = ii) 27) i) ii) iii) b) c) Initial K.E. = 1 mv 2 2 Changed K.E. = 1 v m 2 2 2 (When speed is halved) 1 1 1 1 mv 2 = initial K.E. K.E. becomes th of the original kinetic energy. 4 2 4 4 d) The man using a staircase is doing work against the pull of gravity. The person coming up by elevator is not doing any work. The lift is doing same work against pull of gravity. 28) In automobiles, eg. truck, while in motion, the chemical energy of the petrol or diesel changes into the mechanical (kinetic) energy, heat energy due to friction and sound energy, heat energy due to friction and sound energy. = Volume 1 of 2 Universal Tutorials X ICSE Physics 45 46 29) Momentum of the body P = m v = 20 5 = 100 kg m/s. Momentum of the body Q = m v = 5 20 = 100 kg m/s. 1 1 100 =1 K.E. of P = mv 2 m = 20 kg. = 20 5 2 = 10 25 = 250 J. 100 2 2 30) 1) When current is drawn from electric cell, the chemical energy gets converted into electric energy. 2) When current is drawn from generator, the mechanical energy is converted into electric energy. Ratio = 31) i) Force exerted by the falling mass = mg = 100 10 = 1,000 N ii) Work done = P.E. of the weight = mgh = 100 10 8 = 8,000 J iii) Power input = Work done 8,000 = = 2,000 W Time taken 4 iv) Efficiency = Power output Power input v) Efficiency = Work done by machine Work done on machine or 75 Power output = 100 2,000 or Power output = 3 2,000 4 Work done by machine 75 = 1000 8000 75 8000 = 6,000 J 100 32) i) The S.I. unit of work is joule (J). ii) Total sum of K.E. and P.E. of a freely falling body is constant. Hence total energy (K.E.+P.E.) at any instant is equal to the potential energy at the top position. Or Work done by machine = i.e. Energy at any instant = P.E., at top = mgh = 1 9.8 5 = 49 J iii) No work is done when a body moves in a circular path. W = FS cos , where is the angle between force and displacement. Here, = 90 and cos 90 = 0 W = FS (0) = 0 33) Here m = 50 g = 0.050 kg; V = 500 m/s 1 1 2 mv 2 = 0.050 (500 ) = 6,250 J. 2 2 ii) K.E. of 6,250 J is destroyed within a distance of 10cm = 0.1 m. If F is the average retarding 6,250 force, then F (0.1) = 6,250 or F = = 62,500 N. 0 .1 34) i) Here mass of man m = 60kg; and Let the velocity of mass = v ms 1 i) K.E. of bullet = Then, K.E. of running man = 1 mv 2 2 1 1 mv 2 = 750 J or 60 v 2 = 750 or V2 = 25 V = 25 = 5 m/s. 2 2 ii) When the body is at the highest point of its motion, its velocity is zero but it is acted upon by a downward acceleration due to gravity. Thus, it will be acted upon by a force due to gravity in the downward direction. Now, Force = 1 9.8 = 9.8 N 46 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 02: Work, Energy and Power 47 35) i) Resultant upward force acting on the block = F mg sin 1.5 150 = 200 30 10 = 50 N = 200 30 30 3 Work done = Force Distance = 50 3 = 150J. ii) 36) i) ii) iii) Potential Energy = mgh = 30 10 1.5 = 450J. Sound energy is converted into electrical energy. Electrical energy is converted into light energy and heat energy. Heat energy is converted into mechanical and sound energy. Work Increase in P.E. mgh 60 10 (30 0.20 ) = = = = 240 W Time Time t 15 b) i) Work is said to be done when the point of application of a force moves through a certain distance in the direction of force. It is measured by the product of the force and the displacement of the point of application of the force in the direction of the force, i.e. 37) a) Power = Work = Force Displacement of point of application in the direction of force W = F.S. It s S.I. unit is joule. ii) When the constant force F acts making an angle with the direction in which the body gets displaced, then work done is given by: W = FS cos iii) If the angle between the force applied and the displacement is 90 , work done is zero. W = FS cos 90 = FS 0 = 0 Example: Centripetal force acting on a body does not do work as force is always directed at right angles to the direction of motion of the body. Volume 1 of 2 Universal Tutorials X ICSE Physics 47 48 Chapter 03: Machines Definition Uses Important Terms Principle of a machine Relation connecting efficiency ( ), MA and VR Types of Machines Levers Types of levers Mechanical Advantage of levers Inclined Plane Pulleys Single fixed Pulley Single Movable Pulley Combination of Pulleys Block and Tackle System of pulleys Gears Definition: A machine is a device used to overcome a large resistive force by applying a small force, or to gain speed or to change the direction and the point of application of the force. Any system that changes the relationship between load and effort is called a simple machine. Uses of Simple Machines: As force multipliers (Small force can be used to overcome large force eg. crowbar) To change the direction of force. eg. single fixed pulley To increases speed. eg. gear To change the point of application of the force. eg. Wheel arrangement. Important Definitions: Load and effort z The resistive force to be overcome by a machine is called load (L). z The force applied on the machine to overcome the load is called effort (E). z S.I. unit is newton. Mechanical advantage (MA) L z Mechanical Advantage (MA) is the ratio of load to the effort applied. MA = . E 48 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 03: Machines 49 Velocity ratio (VR). z Velocity Ratio (VR) is the ratio of the velocity at which the effort moves to the velocity at which the load moves. z VR = VE VL or It is the ratio of displacement of effort to the displacement of the load in a given time (VR = dE ). dL Efficiency of a machine ( ). z Efficiency ( ) is defined as the ratio of output work to input work = Note: = work output . work input work output 100 % work input Principle of a machine: z Work output = work input for ideal machine. There is no dissipation of energy. z In practice, no machine is ideal because The moving parts in it are not perfectly smooth The string is not perfectly elastic. Different parts are not perfectly rigid. Moving parts are not weightless. Hence there is loss of energy and work output is not equal to work input. Relation between efficiency ( ), Mechanical Advantage (MA) and velocity Ratio (VR) z Work output = load displacement of load = L dL z Work input = effort displacement of effort = E dE work output L dL MA z Efficiency ( ) = work input = = E dE VR Note: As < 1, MA < VR. z Differences between ideal machine and practical machine. Ideal machine There is no loss of energy Work out put = work input MA = VR Efficiency = 1 Practical machine There is loss of energy due to friction. Work output < work input MA < VR Efficiency < 1 Types of Machines: Levers: A lever is a straight or bent rigid bar, capable of turning about a fixed point (fulcrum) or an axis. Volume 1 of 2 Universal Tutorials X ICSE Physics 49 50 Levers are classified on the basis of the relative positions of fulcrum (F), load (L) and effort.(E) Principle (Principle of moments): In equilibrium position, clockwise moment of the load about the fulcrum = Anticlockwise moment of the effort about the fulcrum (law of levers) z For an ideal lever, Load Load arm = Effort Effort arm. z Mechanical advantage of a lever, M.A. = Effort arm (law of lever) Load arm Types of levers: In lever of first order Fulcrum is in between Load and effort Eg., See Saw, Scissors, Crowbar Fulcrum is between load and effort Lever of second order Load is between fulcrum and effort Eg., Nutcracker, wheelbarrow Load is between fulcrum and effort Lever of third order Effort is between fulcrum and load Eg., Knife, tongs Effort is between load and fulcrum Mechanical Advantage of Levers: 1st order, M. A = 1 or < 1 or > 1 (because Fulcrum may be at the centre, towards effort or towards load) 2nd order, M. A > 1 (because load arm is smaller than effort arm) 3rd order, M. A < 1 (because load arm is greater than effort arm) Examples of each class of levers as found in the human body: Class I lever in the action of nodding of the head. Class II lever in raising the weight of the body on toes. Class III lever in raising a load by forearm. Inclined Plane: It is a smooth, flat rigid surface inclined at an angle to the horizontal. eg. stair case, a flat plank used for rolling barrels. Mechanical Advantage of Inclined Plane h x sin = MA = x h x VR = h C E R L 1 Load = MA = = L sin sin Effort X =1 Note: Due to friction, is less than 1. L sin A L h L cos B Pulleys: Pulley is a flat circular disc, having a groove along its edge and capable of rotation about an axle. 50 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 03: Machines 51 Single fixed pulley z A pulley which has a fixed axis of rotation is called a fixed pulley. L T = =1 E T T z A single fixed pulley is used to change the direction of the applied force T (effort is applied in a convenient direction) and one can use his own body E(N) weight for the effort. L(kgf) z MA = Single Movable Pulley: H A pulley whose axis of rotation is not fixed in position is called a movable pulley 2T = 2 i.e. force multiplier T When the load moves a distance d, the effort moves a distance 2d. MA = VR = 2d =2 d E T efficiency ( ) = 1 or 100% T=E L Combination of pulleys: The use of these pulleys help to apply the load in the downward direction and the MA remains 2. B T T A Movable Pulley Fixed Pulley T2 T(=49N) E(=49N) T2 T T1 W Load L(=10 kgf) C B A E T1 L Load L is balanced by 2T1 in pulley A. T is balanced by 2T2 in pulley B. L = 2 2T2 = 4 T2 MA = E = T2 L 4T2 =4 = E T2 In general if there one n number of movable pulleys, MA = 2n Differences between single fixed and single movable pulley. Single fixed pulley Single movable pulley It fixed to a rigid support. It is not fixed to a rigid support Its mechanical advantage is 1. Its mechanical advantage is 2. Its is velocity ratio is 1. Its velocity ratio is 2. The weight of pulley itself does not affect its mechanical advantage. The weight of pulley itself reduces its mechanical advantage. It is used to change the direction of effort (with its help, effort is applied downwards while without it, effort needed to lift is to be applied upwards.) It is used as a force multiplier. Volume 1 of 2 Universal Tutorials X ICSE Physics 51 52 Block and Tackle System of Pulleys: A block and tackle system consists of two blocks each containing a number of pulleys. The upper block is fixed and the lower one is movable. The fixed block is called block and the movable one is called the tackle. A single light, flexible and inextensible string is passed around all the pulleys. The load (W) acts downwards and tension acts upward. The number of segments of string is equal to the number of pulleys. This system works as a force multiplier. In equilibrium W = nT and T = E W nT = =n E T Where n is the number of pulleys (Ideal) MA = Note: If w is weight of pulleys, then L + w = nT and E = T MA = L + w nT L w n w = = n or + = n or E E T E E VR = n Efficiency = 1 w nE For greater efficiency, pulleys in the lower block should be as light as possible and friction should be reduced by lubricants. Gears: A gear is a wheel with teeth around its rim. Each tooth of a gear acts like a small lever. The gear wheel closer to the source of power is called the driver or the driving gear while the gear wheel which receives motion from the driver is called the driven gear. If the gears make internal contact, both gears rotate in the same direction. Gears can be classified according to the relative positions of the axes of rotation. The velocity ratio of a pair of gears is defined as the ratio of the number of rotations per unit time of the driving (or input) gear to the number of rotations per unit time of the driven (or output) gear i.e. V.R. = V.R. = Numberof rotations per sec ond of the driving gear Number of rotations per sec ond of the driven gear Speed of rotation n A of driver Speed of rotations nB of driven If rA and rB respectively be the radii of the driver and driven wheels, then the ratio of speed of rotation of driver to the speed of rotation of driven is equal to the ratio of the radius of driven wheel to the radius of driver wheel, i.e. V.R. = 52 n A rB = nB rA Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 03: Machines But 53 rB N = B , if NA and NB are respectively the number of teeth in the driving gear and driven rA N A gear Velocity ratio = NB NA This is the fundamental principle of gear tooth action. Thus, number of teeth (NA, NB), radii (rA, rB) and speed of rotation (nA, nB) are related as nA N r = B = B nB N A rA The ratio of number of teeth in the driving wheel to the number of teeth in the driven wheel is called the gear ratio. NA A gear system is used both for the gain in speed as well as for the gain in NB turning effect or torque. In vehicles, going uphill we use the gear system to obtain gain in torque but while going downhill we use it to obtain gain in speed. To produce a desired torque (or speed), a group of two or more gears which work together, is used. Such a system of gears is called a train. A gear system is used to increase the turning effect when the smaller wheel drives the bigger wheel i.e., the driven gear has more number of teeth than the driving gear (i.e., when NB > NA or the gear ratio is less than 1). While ascending a hill an automobile driver changes the gears and puts the driving gear of less number of teeth with a driven gear of more number of teeth. He does so, to obtain gain in torque because more torque is required to go up the hill than to move along a level road. A gear system is used to increase the speed when the bigger wheel drives the smaller wheel i.e. the driving gear has more number of teeth than the driven gear. Gear ratio = Gain in speed = Speed of rotation of driven wheel nB Number of teeth in driving wheel N A = Speed of rotation of driving wheel n A Number of teeth in driven wheel NB A toy motor car used the gear principle to gain speed. It has a key and spring on the axle fitted with a driving gear having more teeth which engages the driven gear having less teeth. The wheels of the car are fitted on the axle of the driven gear. When the key is turned clockwise, the spring turns the driving gear anticlockwise which in turn rotates the wheel of the toy car clockwise at a greater speed. If NA = NB (i.e. gear ratio is 1), there is neither gain in torque nor gain in speed. Application of gear system in watches In a watch, the gear system is used to obtain gain in torque. Ratio of number of rotation of minutes to second hand is 1 : 60 and hour to minute hand is 1 : 12. REVIEW QUESTIONS: Direct questions: 1) State four ways in which machines are useful to us. 2) Give an example for each of the following uses of a machine: a) to obtain gain in force, b) to change the point of application of force, c) to change the direction of force, d) to obtain gain in speed Volume 1 of 2 Universal Tutorials X ICSE Physics 53 54 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) Explain the term mechanical advantage. State its unit Define the term velocity ratio. State its units Define the term efficiency of a machine Define the terms mechanical advantage, velocity ratio and efficiency as applied to a machine. Name the term that will not change for a given design. Derive the relationship between the three terms What is a lever? State its principle Write down a relation expressing the mechanical advantage of a lever Name the three classes of levers and distinguish between them. Give two examples of each class Give one example each of a Class I lever where mechanical advantage is (a) more than one, and (b) less than one. What is the use of the lever if its mechanical advantage is less than 1? Which type of lever has a mechanical advantage always more than one? Give one example. What change can be made in this lever to increase its mechanical advantage? Draw a diagram of a lever which is always used as a force multiplier. State the kind of lever which always has the mechanical advantage less than 1. Draw a labeled diagram of such lever. Explain why the M.A of the Class III type of lever is less than one. Why are they then used? What is an inclined plane? Give two examples where it is used to raise a heavy load with less effort. Write expression for the mechanical advantage of an inclined plane in terms of its length l and vertical height h. What is a gear system? Explain its working. Define the following terms in reference to a gear system a) driving gear b) driven gear c) gear ratio d) gain in speed e) gain in torque What is a single movable pulley? What is its mechanical advantage in the ideal case? Name the type of single pulley that can act as a force multiplier. Draw a labelled diagram of the pulley mentioned by you. Differentiate between a single fixed pulley and a single movable pulley. Name the machine which is used to: a) multiply force, (b) multiply speed, and (c) change the direction of force applied. NUMERICALS: Class Work: 1) A 4 m long rod of negligible weight is to be balanced about a point 125 cm from one end. A load of 18 kgf is suspended at a point 60 cm from the support on the shorter arm. a) A weight W is placed 250 cm from the support on the longer arm. Find W. b) If W = 5 kgf, where must it be kept to balance the rod? c) To which class of lever does it belong? [a) 4.32 kgf (b) 2.16 m from support on longer arm (c) Class I] 2) A force of 5 kgf is required to cut a metal sheet. A shears used for cutting the metal sheet has its blades 5 cm long, while its handle is 10 cm long. What effort is needed to cut the sheet? [2.5 kgf] 3) A man uses a crowbar of length 1.5 m to raise a load of 75 kgf by putting a sharp edge below the bar at a distance 1 m from his hand. Draw a diagram of the arrangement showing the fulcrum (F), load (L) and effort (E) with their directions, Calculate: 54 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 03: 0 Machines s 55 (i) load arm, ( effort arm (ii) m, (iii) mechanica al advantage and ( the effort (iv) t needed. Sta ate the kind o of lever. [ (i)0.5 m (ii) ) 1.0 m (iii) 2 (iv) 37.5 kgf f. Class I] 4) If the weight of wheel barrow is 15 kg gf and the we eight of s sand in it is 60 6 kgf, use th he informatio on given in to o c calculate the e minimum ef ffort required d to keep the e leg just [25 kgf] o the groun off nd. 5) Th he diagram below b shows a lever in us se. a) To which cla ass of lever does d it belon ng? b) If FA = 80 cm, AB = 20 cm, c find its M.A M c) Calculate the value of E. [(a) Cla ass II (b) 1.25 5 (c) 4 kf] 6) A fire f tongs ha as its arms 20 0 cm long. It is used to lif ft a coal of weight w 1.5 kgf by applying g an effort at distance 15 5 cm from the e fulcrum. Find: i) the mechanical m ad dvantage of fire tongs an nd (ii) the eff fort needed. [ (i) 0.75 ii) 2.0 kgf] 7) A coolie uses a sloping wo ooden plank of o length 2.0 0 m to push up u a drum of f mass 100 kg k into the tru uck at a height 1.0 m. a) What is the mechanical advantage of o the sloping g plank? b) How much effort e is need ded to push the t drum up into the truck k? c) What assum mption have you y made in arriving at th he answer in part (b) abo ove? [a) 2 (b b) 50 kgf] 8) A gear system has the driv ving wheel of f radius 2 cm m and driven wheel w of radius 20 cm. a) Find the gea ar ratio b) If the numb 0, find the number ber of rotatio ons made pe er minute by the driving wheel is 100 n of rot tations per minute m made by the driven wheel. c) If the driven wheel has 40 4 teeth, find d the number r of teeth in th he driving wh heel. [a) 1:10 (b) 10 (c) 4] 9) A woman w draw ws water from m a well using a fixed pul lley. The mas ss of bucket and water to ogether is 6 kg. The fo orce applied d by the woman is 70 0 N. Calcul late the me echanical ad dvantage. (Take g = 10 m s 2) [0.875] 10) In a block and tackle syste em consisting g of 3 pulleys s, a load of 75 7 kgf is raise ed with an ef ffort of 25 kg gf. Find the mechanical m ad dvantage, ve elocity ratio and a efficiency y. [3, 3, 100%] 11) A pulley system has a velo ocity ratio 3 and an effici iency of 80% %. Draw a lab belled diagra am of this pu ulley system. . Calculate the t mechanical advantag ge of the sy ystem and th he value of the effort req quired to rais se a load of 300 3 N. .4, 125 N [2. 12) A block and tackle t system m has the velocity v ratio o 3. Draw a labelled dia agram of the system dicating the points p of app plication and the direction ns of load an nd effort. A m man can exer rt a pull of ind 20 00 kgf. What is the maxim mum load he can raise wi ith this pulley y system if its s efficiency is 60%? [360 kgf] Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 55 56 g shows a block and tack kle system of f pulleys use ed 13) Fig to lift a load. a) How many strands of ta ackle are sup pporting the load? b) Draw arrow ws to represe ent tension in n each strand d. c) What is the e mechanical advantage of o the system m? d) When load is pulled up by a distanc ce 1 m, how far doe es the effort end e move? [(a) 4 (c) 4 (d) 4m] Home Work: W 1) A crowbar of length 120 cm has its fulcrum situ uated at a distance of 2 20 cm from the load. [5] alculate the mechanical m a advantage of f the crowbar r. Ca 2) A pair of scissors has its s blades 15 cm long, wh hile its hand dles are 75 cm long. What W is its me [0.5] echanical ad dvantage? 3) Th he diagram below b shows a lever in us se. a) To which cla ass of lever does d it belon ng? b) If AB = 1 m, AF = 04 m, find its mech hanical adva antage. [(a) clas c) Calculate the value of E. ss I (b) 1.5 (c c) 10kgf] 4) A pair of sciss sors is used to t cut a piec ce of a cloth by keeping it at a distan nce 2 cm from m its rivet an nd applying an a effort of 10 0 kgf by finge ers at a dista ance 8 cm fro om the rivet. Find: i) the t mechanic cal advantag ge of scissors s and ii) the load offe ered by the cloth. c How does d the pair r of scissors act : as a fo orce multiplie er or as a sp [(i) peed multiplie er? ) 0.25 (ii) 40 kgf speed multiplier] m 5) Th he fig below w shows a wheel barro ow of mass s 15 kg ca arrying a load d of 30 kgf with w its centre e of gravity at t A. The po oints B and C are the centre c of wheel and tip p of the ha andle such th hat the horiz zontal distanc ce AB = 20 cm and AC C = 40 cm. a) In the diagr ram mark ful lcrum F, load d L and effor rt E with their directions b) Calculate : i) the load arm, a ii) the effort t arm iii) the mech hanical adva antage and iv) the minim mum effort re equired to ke eep the leg ju ust off the gr round. c) Name the kind k of lever. [(b) i) 20 cm ii) 60 cm, iii) 3 iv)15 kgf (c) Class II] 6) Th he diagram shows s the use of a lever. a) State the principle p of moments m as applied to the t above lev ver. b) Give an exa ample of this class of leve er c) If FA = 10 cm, AB = 500 5 cm, calc culate the mechanical m 1 dvantage and d the minimum effort requ uired to lift th he load. effort = 2550 N] [(c) M.A = ad 51 7) A boy has to lift a load of f mass 50 kg k to a heigh ht of 1 m. What W effort is s required if he lifts it dir rectly 7 Take e g = 10 N kg 1. But he e can exert a maximum m effort of 25 50 N, so he e uses an inc clined plane to lift the loa ad up. What should s be the e minimum le ength of the plank used by b him? [500 0 N, 2 m] 56 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 03: 0 Machines s 57 8) A gear system m has one wh heel with 10 teeth t and the e other whee el with 50 tee eth. Calculate e the gain in speed and the t gain in torque t that you y can obta ain using the em. What will be the gea ar ratio in ea ach case? [Gain in speed = 5, gear ratio 5:1; gain in torque = 5 5, gear ratio = 1:5] 9) Th he driving wh heel of a gea ar system is of o radius 16 cm and it ha as 32 teeth. F For one rotat tion of the dri iving wheel, if the driven wheel make es four rotatio ons, find: i) the t radius, and ii) the num mber of teeth h in the drive en wheel [(i) 4 cm (ii) 8] 10) A fixed pulley is driven by a 100 kg mass falling at a a rate of 8 0 8 m in 40 s s. It lifts a loa ad of 500 kg gf. Calculate the power input to the pulley taking g the force of o gravity on 1 kg as 10 0 N. If the eff ficiency of the pulley is 75 5%, find the height to wh hich the load is raised in 4 4.0 s. [2000W W, 1.2 m] 11) A block and ta ackle system has 5 pulley ys. If an effort of 1000 N is needed to o raise a load of 4500 N, calculate: a) mechanical advantage b) velocity v ratio o, and c) efficiency of [a) 4.5 (b) 5 (c) 90%] f the system. 12) In fig. draw a tack kle to lift a load by app plying the fo orce in a co onvenient direction. Mark the position p of lo oad and effor rt. a) If the e load is raise ed by 1 m, th hrough what distance will l the effort move? m b) State e how many strands of ta ackle are sup pporting the c) What t is the mech hanical advantage of the system? [a) 5 m (b b) 5 (c) 5] 13) Fig g shows a system s of fou ur pulleys. The T upper tw wo pulleys ar re fixed and the low wer two are movable. m a) Draw a strin ng around the e pulleys. Als so show the place and direction in wh hich the effort is applied. b) What is the velocity ratio o of the syste em? c) How are loa ad and effort of the pulley y system rela ated? d) What assum mption do you u make in ar rriving at your answer in part p (c) ? [b) 4 (c) load = 4 effort] APPLICATION TYPE: T Class Work: W 1) Why is a mach hine not 100% % efficient? 2) What is the relationship be etween the mechanical m ad dvantage and d the velocity y ratio for a) an ideal machine b) a practical machine m 3) Ex xplain why sc cissors for cutting c cloth may have blades longer r than the ha andles, but shears s for cu utting metals have short blades b and lo ong handles. 4) Th he diagram shows s a type of nut crack ker. a) In the diagra am, i) Show with the t letter F, the t position of o the fulcrum m ii) Draw an arrow marked L, to show th he direction and a line of action of the resistance (load) iii) Draw an arrow, marked d E to show the direction and likely the e point of ap pplication of the effort b) What class of lever is the nut cracke er shown in th he diagram? 5) Dr raw a labelled diagram of f a Class II le ever. Give on ne example of o such a lev ver. Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 57 58 6) To o which class s of levers do o the followin ng belong? c) Crowbar a) Wheel barro ow b) Nut cracker C d) F Fishing rod e) Forearm f) Fire F tongs g) Physical bala ance h) S Seesaw i) Rowing k) Opening R oar of o a boat j) Forceps F O a door l) O Opening a bo ox m) ) Motor car fo oot brake n) Knife 7) Give an examp ple each whe ere a gear sy ystem is used d to obtain a) a gain in torq que b) gain in n speed 8) In a single fixe ed pulley, if th he effort mov ves by a dist tance x down nwards, by w what height is s the load rai ised upwards s? 9) In which direc ction the forc ce need be applied, whe en a single pulley is use ed with a mechanical ad dvantage gre eater than on ne? How can n you change e the directio on of force ap pplied withou ut altering its mechanical advantage? ? 10) Th he diagram below b shows a pulley arra angement. a) In the diag gram, mark the direction n of the for rces due to tension, acting on th he pulley A. b) What is the e purpose of the pulley B? ? c) If the tensio on is T Newto on, deduce the relation between b T an nd E. d) What is the e velocity ratio of the arrangement? e) Assuming that t the efficiency of the system s is 100% What is the me echanical advantage? 11) Dr raw a diagra am of a bloc ck and tackle e system of f pulleys hav ving a velocity ratio of 5. 5 In your dia agram indica ate clearly th he points of application and a the direc ctions of the e load and ef ffort. Also ma ark the tensio on in each st trand. 12) To o which order the followin ng levers belo ong and why y? i) Railway R sign nal ii) a man cutting g bread with knife iii) a boy writing on a piece e of paper iv) nut cracker v) handle of wa vi) see saw ater pump vii) fore ceps viii) a man rowi ing boat ix) x) opener ) lock and ke ey o of a soda s water b bottle xi) ) closing a do oor xii) ) motor car fo oot brake xiii) nail cutter xiv) a fishing ro od xv v) a lemon sq queezer 13) Diagram show ws a nut crack ker with a fix xed base. In the t diagram: i) Mark M the letter F for fulc crum, ii) Mark by an arrow a the dir rection in which resistanc ce acts. iii) Mark by an arrow the direction in wh hich effort ac cts, iv) ) How can yo ou increase efficiency e of nut n cracker? iv) ) By increasin ng effort arm m. Home Work: W 1) State the relati ionship betw ween mechan nical advanta age, velocity ratio and eff ficiency. 2) A pair of scisso ors and a pa air of pliers both b belong to the same class c of leve ers. Name the e class of ver. Which one has the M.A M less than n 1? lev 3) In Fig. a unifo orm metre scale s is kep pt in equilibrium when su upported at the t 60 cm mark m and a mass m M is suspended s fro om the 90 cm m mark. Stat te with reaso on whether the t weight of the scale is greater than n, less than or o equal to the weight of mass m M. 58 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 03: 0 Machines s 59 4) Th he diagram below b shows s a wheel ba arrow. In the diagram ma ark the e fulcrum. Al lso draw arro ows to show w the directions of load an nd eff fort. What cl lass of lever r is the whee el barrow? Give G one mo ore ex xample of the e same class s of lever. 5) Ind dicate the po ositions of loa ad, effort and d fulcrum in the t forearm shown. s 6) St teeper the in nclined plane e more is the effort neede ed to push a load up the p plane . Expla ain it. 7) Th here is no ga ain in mecha anical advant tage in the case c of a sin ngle fixed pulley. Explain, why the pu ulley is then used? u 8) Give two reaso ons why the efficiency of a single mov vable pulley system is no ot 100%. how how a single s pulley can be used d to reduce the effort required to ov vercome a given load. 9) Sh Dr raw a diagram of the sys stem. Why is s it generally y more conve enient to use e two pulleys s for this? Na ame the two pulleys. 10) Th he diagram below b shows s an arrange ement of thre ee pulleys A, , B and C. Th he load is ma arked as L an nd the effort as E. a) Name the pulleys p A, B and a C. T T b) Mark in the e diagram th he directions of load (L), effort (E) an nd tension T (T) in each string. c) How are the e magnitudes of L and E related to th he tension T? ? T d) Calculate the mechan nical advan ntage and velocity rati io of the arrangemen nt. e) What assum mptions have e you made in parts (c) and a (d)? 11) Give reasons for f the follow wing: a) In a single fixed f pulley, the velocity ratio is alway ys more than n the mechan nical advanta age. b) The efficien ncy of a pulle ey is always less than 100%. c) In case of a block and d tackle arra angement, th he mechanic cal advantag ge increases s with the increase in the number of pulleys. d) The lower block b of a blo ock and tackle pulley system must be e of negligible e weight. 12) Fig gure shows a diagram of f a system of o four pulley ys. The upper two pulleys s are fix xed and the lo ower two are e movable. a) Draw a strin ng around th he pulleys. Also show the e place and direction d in w which the effort is applied. b) Draw an arrow to repres sent tension in each strand. c) What is the e mechanical advantage of o the system m? d) What is the e velocity ratio o of the system? e) What assum mption do yo ou make in ar rriving at you ur answer in part (a)? 13) Fig gure shows a wheel barrow. a) Mark the fulcrum. b) Mark the direction and point p of actio on of effort. c) State the class of lever it belongs to o. d) Give one more m example e of this type of lever. Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 59 60 MISCELLANEOUS: 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 60 What do you understand by a simple machine? What is the purpose of a jack in lifting a car by it? What do you understand by an ideal machine? Mechanical advantage (M.A), load (L) and effort (E) are related as: a) M.A = L E b) M.A E = L c) E = M.A L d) None of these The correct relationship between the velocity ratio (V.R) distance moved by load (dL) and distance moved by effort (dE) is b) V.R = dL/dE c) V.R. = dE/ dL d) V.R. = dE dL a) V.R> = dL + dE The correct relationship between the mechanical advantage (M.A), the velocity ratio (V.R) and the efficiency ( ) is: a) M.A = V.R b) V.R. = M.A c) = M.A V.R d) None of these For an ideal machine, the ratio of mechanical advantage (M.A.) to the velocity ratio (V.R.) is a) greater than one b) less than one c) equal to one d) depends on the value of load Which of the following statements is not true for a machine a) It always has efficiency less than 100% b) Mechanical advantage can be less than one c) It can also be used as a speed multiplier d) It can have a mechanical advantage greater than the velocity ratio Class I lever is that in which: a) fulcrum is between the load and effort b) load is between the fulcrum and effort c) effort is between the load and fulcrum d) fulcrum, load and effort are at one point Explain why the M.A. of a Class II type of lever is always more than one. What type of lever is formed by the human arm while raising a load from a table placed in front? Where is the position of the fulcrum? Draw a labeled sketch of a Class III lever. Give one example of this kind of lever. Give example of each class of lever in a human body. The lever for which the mechanical advantage is less than one has: a) fulcrum at mid point between load and effort b) load between effort and fulcrum c) effort between fulcrum and load d) load and effort acting at the same point Draw diagrams to illustrate the positions of fulcrum load and effort, in each of the following: a) A seesaw b) A common balance c) A nut cracker d) Forceps The force needed to push a load up an inclined plane is less than the force needed to lift it directly . Give a reason. State whether the mechanical advantage of an plane is equal to 1, less than 1 or greater than 1? Explain how a gear system can be used to gain in speed, and (b) gain in torque. What is a fixed pulley? Give one use of a single fixed pulley. What is the ideal mechanical advantage of a single fixed pulley? A single fixed pulley is used because it: a) has a mechanical advantage greater than 1 b) has a velocity ratio less than 1 c) gives 100% efficiency d) helps to apply the effort in a convenient direction. Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 03: Machines 61 23) In a single movable pulley, if the effort moves by a distance x upwards, by what height is the load raised? 24) Draw a labelled diagram of an arrangement of two pulleys, one fixed and other movable. In the diagram, mark the directions of all forces acting on it. What is the ideal mechanical advantage of the system? How can it be achieved? 25) What is a block and tackle system of pulleys? 26) For greater efficiency of a block and tackle pulley system: a) the lower block should be of negligible b) the upper and lower blocks should be of equal weights c) the lower block should be heavier than the upper block d) the weight of rope should be equal to the weight of pulleys. 27) State whether the following statements are true or false. a) The velocity ratio of a single fixed pulley is always more than 1. b) The velocity ratio of a single movable pulley is always 2. c) The velocity ratio of a block and tackle system is always equal to the number of strands of the tackle supporting the load. 28) a) Name six simple machines. b) Give one practical example of each machine named in (a). 29) Define the following terms with reference to a machine; i) load ii) effort iii) ideal machine iv) mechanical advantage v) velocity ratio vi) efficiency 30) Give the principle of a machine. 31) Prove that efficiency of a machine is the ratio between mechanical advantage and velocity ratio. 32) Give two reasons why a machine cannot be 100% efficient. 33) (a) Define lever (b) What are its three kinds? (c) How will you determine the order of lever? 34) a) Why lever of second order has mechanical advantage more than 1? b) Why lever of third order has mechanical advantage less than 1? 35) Figure shows a diagram consists of 5 pulleys. a) Copy the diagram and complete it by drawing a string around the pulleys. Mark the position of load and the effort. b) If the load is raised by 1 m, through what distance will the effort move? 36) Explain why the cutting edges of scissors are made longer as compared to cutting edge of metal cutter? 37) a) What is a pulley? b) Mechanical advantage of a single fixed pulley is always less than 1. Why is this pulley commonly used? 38) Draw a neat diagram of a pulley system with velocity ratio 6. 39) Draw a diagram of single movable pulley system. Why is this system preferred to single pulley system? 40) A uniform see saw is 5 m long and is supported at its centre. A boy weighing 40 kg sits one meter from the centre of see saw. Where must a girl weighing x 25 kg sit from the centre of see saw so as to balance the B A 1m 25 kg 40kg weight of boy? Volume 1 of 2 Universal Tutorials X ICSE Physics 61 62 41) A handle of nut cracker is 16 cm long and a nut is placed two centimeter from its hinge. If the force of 4 kg is applied at the end of handle to crack it. What weight if simply placed on nut cracker will crack it? 16cm 4cm 2cm 42) An effort of 10 kgf is applied at the end of a lever of second order which supports a load of 750 kgf, such that load is at a distance of 10 cm from the hinge. Find the length of lever. (Assume lever is weightless). 43) An effort of 5 kgf is applied on machine through a distance of 80 cm when a load of 80kgf moves through a distance of 4 cm. Find (i) velocity ratio (ii) mechanical advantage (iii) efficiency. 44) A machine is 60% efficient and has a velocity ratio 4. Find its (i) mechanical advantage (ii) effort required, if load lifted is 1000 kgf. 45) An effort of 500 N is applied through a distance of 50 cm. If the efficiency of machine is 90% and load moves through a distance of 4 cm find (i) velocity ratio, (ii) mechanical advantage, (iii) useful load lifted. 46) A crow bar of length 2 meters is used to lift a heavy box of 2m mass 100 kg by placing a fulcrum at a distance of 10 cm from 190 cm E one of its ends. Find effort required at the other end so as to L 10 cm F lift the load. 47) A person is carrying a load of 20 kgf, which is projecting 25 cm from his shoulder. How far from the shoulder the person should apply 8 kgf forces, so as to balance the rod carried by him? 48) The diagram shows a pulley arrangement. i) In the diagram, mark the direction of force due to tension acting on the movable pulley. ii) What is the purpose of the fixed pulley? iii) If the tension is T newton, deduce the relation between T and E. F iv) Calculate the effort. v) Assuming that the efficiency is 100%, what is the mechanical advantage? 100N vi) State two factors that would reduce the efficiency of the arrangement. 49) Calculate the size of the force E which will just lift the total weight of 200 N acting on the wheel barrow as shown in the adjacent diagram. If E is raised 25 cm in 0.5 second, calculate the work done and the average rate of working. 50) 62 A pulley system has four pulleys in all and is 80% efficient. Draw the net diagram of pulley system and calculate i) mechanical advantage, ii) effort required to lift a load of 1500 N, iii) wt of movable part. Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 03: 0 Machines s 63 51) A pulley system m has five pu ulleys in all and a is 90% efficient. Calc culate i) mechanical m a advantage, ii) load lifted by y an effort of f 1000 N. iii) wt of movab ble parts of machine. m 52) A pulley system lifts a load d of 1200 N by an effort of 250 N. If the load due to movable e parts of ma achine etc is s 300 N, find d (i) Actual Mechanical M Advantage A (ii) I.M.A. (iii) v velocity ratio o (iv) total nu umber of pulleys in system m (v) efficien ncy of system m. 53) A pulley system m can lift a load of 1000 N, by an eff fort of 240 N. N If the load due to mova able parts of machine etc c is 200 N, fin nd (i) A.M.A. (ii) I.M.A. (iii) V.R R. (iv) efficien ncy (v) numb ber of pulleys s in system. 54) Th he gradient of o a hill road d is 1 : 80. Calculate C the weight of th he vehicle w which is push hed up an inc cline by an effort e of 150 kgf. k PREVIOUS S BOARD QU UESTIONS: 1) i) State S the cla ass of levers and the relative positions s of load (L), , effort (E) an nd fulcrum (F F) in each of the following g case: 1. A bottle opene er, 2. Sugar to ongs. s effort needed to lift a lo oad over an inclined plan ne as compa ared to lifting g the load ii) Why is less [2012] directly? nder what co ondition will a set of gears s produce (a) a gain in sp peed, (b) a g gain in torque e? 2) Un [2012, 1M] en a nut by applying a a fo orce of 150N by using a le ever handle of length 0.4 4 m. What 3) A man can ope sh [2011] hould be the length of the e handle if he e is able to op pen it by app plying a force e of 60 N? 4) Na ame a machi ine which ca an be used to o (i) multiply force f (ii) cha ange the dire ection of force e applied. [2011] Effort (E E) he diagram below b shows a lever in us se: 5) Th A F i) To which cl lass of lever does it belon ng? B c AB = 60 cm, then find d the ii) If FA = 40 cm, Load (L) mechanical l advantage of the lever. [2011, 2] 50N eant by an ide eal machine? ? 6) i) What is me ationship bet tween the mechanical ad dvantage (M.A.) and velo ocity ratio (V.R.) of an ii) Write a rela ideal machi ine. d on his head d and moving on a frictio onless horizo ontal platform m does no iii) A coolie carrying a load work. Expla [2011] ain the reaso on why. erms mechan nical advanta age, velocity ratio and eff ficiency of a machine, 7) i) With reference to the te name: the term t that will not change for a machin ne of a given n design. t stated by b you in par rt (1) [2009] ii) Define the term 8) Co opy the diagr ram of the fo orearm given below, ind dicate the po ositions of Load, Effort an nd Fulcrum raw a labelle ed diagram of o a block and tackle system of pulley ys with two p pulleys in ea ach block. 9) Dr [2008] Ind dicate the dir rections of th he load, effor rt and tension in the string. 10) Write down the e relation bet tween the loa ad and the effort e of the pulley p system m. [2008] f levers has a mechanica al advantage e always gre eater than on ne? What change can 11) Which class of e brought abo out in this lev ver to increas se its mecha anical advant tage? be [2007] 12) Write an expre ession to sho ow the relationship between mechan nical advanta age, velocity ratio and eff ficiency for a simple mac chine. [2007] Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 63 64 13) A block and tackle pulley system has a velocity ratio 3. i) Draw a labeled diagram of this system. In your diagram, indicate clearly the points of application and the directions of the load and effort. ii) Why should the lower block of this pulley system be of negligible weight? (2007) 14) A uniform metre scale is kept in equilibrium when supported at the 60 cm mark and a mass M is suspended from the 90 cm mark as shown in the figure. State with reasons, whether the weight of the scale is greater than, less than or equal to the weight of mass M. (2006) 15) Name the type of single pulley that can act as a force multiplier. Draw a labelled diagram of the above named pulley. 16) A pulley system has a velocity ratio of 4 and an efficiency of 90%. Calculate (i) the mechanical advantage of the system. (ii) the effort required to raise a load of 300 N by the system. [3.6, 83.33 N] 17) a) i) Define an Inclined plane. ii) Draw a labeled sketch of a class II lever. Give one example of such a lever. P2 b) The alongside figure shows the combination of a movable pulley P1 T T T with a fixed pulley P2 used for lifting up a load W. P1 C i) State the function of the fixed pulley P2 ii) If the free end of the string moves through a distance x, find the distance by which the load W is raised. W iii) Calculate the force to be applied at C to just raise the load W = 20 Load [10 kgf] kgf, neglecting the weight of the pulley P1 and friction. 18) i) Explain why scissors for cutting cloth may have blades much longer than the handles; but shears for cutting metals have short blades and long handles. ii) A woman draws water from a well using a fixed pulley. The mass of the bucket and water together is 6.0 kg. The force applied by the woman is 70 N. Calculate the mechanical [0.86] advantage. (Take g = 10 m/s2) 19) What is the relationship between the mechanical advantage and the velocity ratio for: i) An ideal machine ii) A practical machine? 20) A cook uses a fire tong of length 28 cm to lift a piece of burning coal of mass 250 g. If he applies his effort at a distance of 7 cm from the fulcrum, what is the effort in S.I. unit? [Take g = 10 m/s2] [10 N] 21) To use machine as a force multiplier, what type (class) of lever should preferably be used? Draw a sketch of such a lever. 22) A pair of scissors and a pair of pliers belong to the same class of levers. i) Which one has mechanical advantage less than one? ii) State the usefulness of a machine whose mechanical advantage is less than one. 23) Why is the mechanical advantage of a lever of the third order always less than 1? Give one example of this class of lever. 24) In the diagram of a stationary wheel barrow, the centre of gravity is at A. The wheel and the leg are in contact with the ground. The horizontal distance between A and F is 50 cm and that between B and F is 150 cm. i) What is the direction of the force acting at A.? Name the force. ii) What is the direction of the minimum force at B to keep the leg off the ground? What is this force called? 64 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 03: Machines 65 iii) The weight of the wheel barrow is 15kgf and it holds sand of weight 60 kgf. Calculate the minimum force required to keep the leg off the ground. [25 kgf] 25) i) Which class of levers has a mechanical advantage always less than L F one? Explain briefly with a diagram why their mechanical advantage is less than one. E ii) The crow bar is a type of lever as shown alongside: A crow bar of length 150cm has its fulcrum at a distance of 25cm. from the load. Calculate the mechanical advantage of this crow bar. [5] Effort B 26) The diagram along with shows the use of a lever. Fixed i) State the principle of moments as applied to the lever. F A ii) Give an example of this class of lever. iii) If FA = 10 cm, AB = 500 cm, Calculate the minimum effort required to lift the load. Load 50N [2550 N] 27) The diagram alongside shows a system of 5 pulleys. i) Copy the diagram and complete it by drawing a string around the pulleys. Mark the position of load and the effort. ii) If the load is raised by 1 m, through what distance will the effort move? [5M] 28) Diagram 1 alongside shows a weightless lever in equilibrium. Neglect friction at the fulcrum F. i) State the principle of moments as applied to the alongside A F B lever. ii) Define mechanical advantage and calculate its value for the L given lever. E iii) Name the type of lever which has mechanical advantage greater than 1. 29) Diagram alongside gives an arrangement of single moving pulleys. Copy the diagram. If the effort applied at the free end of the string is E, i) Show the direction and magnitude of the forces exerted by the four strings marked (1) to (4). ii) What is the load which can be lifted by the effort? iii) Calculate the mechanical advantage of the system of pulleys. [4] 30) Diagram given alongside shows an arrangement of four pulleys. A load L is attached to the movable lower block and effort E is applied end of at free the string. Copy the diagram and i) Draw arrows to indicate tension in each apart of the string; and ii) Calculate the mechanical advantage of the system. Volume 1 of 2 Universal Tutorials X ICSE Physics [MA= 4] 65 66 ANSWERS: Previous Board Questions: 1) i) 1. A bottle opener: Class II. Load is in between the fulcrum and effort. 2. Sugar tongs: Class III. Effort is in between the fulcrum and load. ii) For an inclined plane, mechanical advantage = L length of inclinedplane (l) = > 1 (since l > h) height(h) E Effort E < load L. 2) a) When bigger wheel drives the smaller wheel (Ndriving > Ndriven) b) When smaller wheel drives the bigger wheel (Ndriving < Ndriven) 4) 1 m 13) (i) Class II (ii) 2 14) M 30 = E 60; M = 2E; scale weight is less 16) MA = 3.6; E = 83.33N An inclined plane is usually a smooth, flat rigid surface inclined at an angle ( ) to the horizontal. It is used to raise heavy loads with relatively small force. The longer the slope, the smaller is the effort needed. ii) A labelled diagram of a class II lever is given below. Its example is a nutcracker. 17) a) i) E (Effort) A E Effort arm F (Fulcrum) Load arm B C L (Load) Second Class Lever b) i) It is quite difficult to apply effort in the upward direction, if no fixed pulley P2 is used. The fixed pulley changes the direction of effort from upwards to downwards, making the effort more convenient and easier. ii) As the movable pulley doubles the effort, Force, L = 2T Mechanical advantage M.A. = i.e., W = 2T Dis tan ce travelled by effort 2x 2T = =2 = 2 and V.R. = Dis tan ce travelled by load x T The distance travelled by load is half the distance moved by effort = x/2 20 = 10 kgf 2 18) i) In case of scissors, blades may be much longer than the handles, because in this case we don t need much mechanical advantage. (M.A. = Effort Arm/Load Arm) But in case of shears for cutting metals, much higher value of mechanical advantage is needed to cut the metals easily, so the handles need to be long and blades short. iii) Since W = 2T or 20 kgf = 2T; Here, T = effort; Effort applied = ii) M.A. = 6 10 60 6 Load = = = = 0.86 Effort 70 70 7 19) 1) Mechanical advantage is equal to velocity ratio. 2) Mechanical Advantage is less than velocity ratio as efficiency is less than one. 20) Effort Effort arm = Load Load arm E 0.07 = (0.250 10) 0.28 66 E= 0.250 10 0.28 = 10 N. 0.07 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 03: 0 Machines s 67 E 21) Le ever of secon nd type (or cl lass) is used as force mu ultiplier. Me echanical ad dvantage of a lever = Effo ort Arm Loa ad Arm F 22) i) A pair of sc cissors and a pair of plier rs belong to first class of f levers. In le evers of this class, c the mechanical l advantage may be equ ual to, less than or grea ater than one. In the ca ase of the given two levers, l the mechanical m a advantage is s more than one. None of the two levers, in general has s mechanical advantage less than on ne. ii) An example e of a machin ne, having mechanical m advantage les ss than I is single fixed pulley. It is useful beca ause it is alw ways easy an nd comfortab ble to apply efforts in the e downward direction rather than n upward dir rection. One e can use own body we eight while a applying effo ort in the downward direction. d 23) In the levers of the third or rder, the effo ort E is in bet tween the ful lcrum F and the load L and a hence the e effort arm is always sm maller than th he load arm, so the mechanical adva antage that is s the ratio be etween the ef ffort arm and d the load a arm is always s less than 1. Example: S Sugar tongs. 24) i) The directio on of force ac cting at A is vertically dow wnwards. Th his force is na amed as Loa ad. ii) The directio on of the min nimum force at B is vertic cally upwards s and is deno oted by E (ef ffort). iii) Total load = (15 + 60) kgf k = 75 kgf, Load arm = 50 cm = 0.5 5 m. Effort arm = 150 cm = 1.5 1 m. To calculate e the minimu um force req quired to keep the leg off the ground. Applying the principle of o lever. 75 0.5 Load Loa E= ad arm = Effo ort Effort ar rm or 75 0.5 = E 1.5 = 25 kgf. 1.5 25) i) In case of levers of third kind, the e mechanical advantage is always le ess than one e. This is because ef ffort arm is always a less than load ar rm. Coal ton ng is an example of leve er of third kind. In the e figure show wn, effort arm m is half of load arm. He ence effort to o be applied d must be double than n load. ii) Here load arm Eff a = 25 cm fort arm = (15 50 25) = 12 25 cm The Mecha anical Advant tage = Effortarm or Load darm M.A M = 125 =5 25 26) i) Principle of f moment sta ates that whe en the body is i in equilibri ium under th he action of number n of forces, the sum of cloc ckwise mome ents is equa al to the Effort clockwise moments. m sum of anti B Fix xed Here, Load Load arm = Effort Ef ffort arm F A (Clockwise) ) (Anti clockwise) ad 50N Loa i.e. L Load (BF) = Effort (AF) ii) This is a lev ver of third kind. An exam mple of this ty ype of lever is jaw or a pa air of tongs. iii) Now, Effort t (AF) = Load d (BF) = Load d (FA + AB) Or Effort t (10) = 50 (1 10 + 500) or o Effort = 5( (510) = 2,550 N. 27) i) The comple ete diagram showing the e string arou und the pulleys is show wn below. Effort is ap pplied in dow wnward direction and th he load moves in upwar rd direction. ii) When the lo oad is raised d by 1 m, the e effort has to t be applied d by 5m sinc ce there are fiv ve segments s of the rope. . Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 67 68 28) i) For equilibr rium, the moment of the effort e about the t fulcrum must m be equa al and oppos site to the moment of the weight (L Load) about it. Therefore e, Effort Eff fort arm = We eight Weig ght arm. wn as the principle of lev ver and mathematically re epresented a as, L BF = E AF This is know ii) Mechanica al Advantage: The mech hanical adva antage of a machine m is d defined as th he ratio of load to effort: M.A. of the given lever = Load AF F = Effort BF F iii) In a lever of the seco ond order, we w always have h effort arm > load arm and hence h the l advantage in this case must m always be greater than t 1. mechanical 29) i) The directio ons of tensio on T are as marked in the diagram and are equ ual in magnit tude. The tension is equal e to T for r the first bloc ck and 2T for the second d block. ii) The effort E can lift a load of 4 time its own magnitude as Lo oad = 2T + 2T T = 4T and T = E. iii) Here W = 4T 4 or W = 4E E M.A. = W =4 E Or M.A. = 4, 4 i.e., twice the t number of o pulleys in the t movable e block. In general if there are n pulleys in th he movable blo ock, M.A. = 2x. 2 30) i) In complete ed diagram alongside a the e arrow head ds are marke ed to indicat te the tension in each part of the string s passin ng over the pulleys. ii) Let n be the number of f segments of o the string which suppo orts the lowe er block, then n = No. of the pulleys in n two blocks = 4 in As there is s only one st tring passing g round all the pulleys, the t tension i each of the segment is the same, i.e e. T = E. Therefore, the total up pward force on the blo ock is 4E and a this mus st balance the e weight L supported by b it, if the weight of lo ower block is L neglected. Thus, T L = 4E E or = 4. E L is called the mechanical m ad dvantage of the t system. E A. = 4. Mecha anical advan ntage of the system s Hence, M.A Now, 68 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 04: Refraction at Plane Surface 69 Chapter 04: Refraction at Plane Surface Refraction Laws Refractive Index Principle of Reversibility of Light Factors affecting refractive index Refraction through Glass Slab Lateral Displacement Multiple images Critical Angle Total Internal Reflection Relation between and c Applications Refraction through Prism Factors affecting angle of deviation Total Reflecting Prisms Difference between ordinary reflection and total internal reflection Refraction: The change in the direction of the path of light, when it passes from one transparent medium to another transparent medium oblique to the surface of separation is called refraction. i) When a ray travels from rarer to denser medium i > r and = i r, is angle of deviation. ii) When the ray travels from denser to rarer medium i < r and = r i Volume 1 of 2 Universal Tutorials X ICSE Physics 69 70 A iii) W When the ray y travels alon ng the norma al to the s surface of se eparation of the two media, i = 0, r = 0, = 0 ( refraction (no n takes place e) S i = 0 AIR (RA ARER) GLASS OR ER WATE (DENSE ER) O INC CIDENT R RAY 90 MEDIUM 1 MEDIUM 2 S r = 0 B REFRACTED RAY Note: : Refraction is a surfac ce phenome enon. Chang ge of mediu um causes p partial reflec ction and transm mission. Note: : Refraction occurs o becau use light trav vels with diffe erent speeds s in different media. There e is a chang ge in wavele ength but no ot in frequen ncy when lig ght passes from one medium m to anoth her. Laws s of Refra action: 1) The incident t ray, the ref fracted ray and the normal at the point of incidence, all lie in the same plane. 2) The sine of f the angle of incidence e bears a constant c rati io with the sine of the angle of refraction for a given pai ir of media and waveleng gth of light. The T second law l is known n as Snell s la aw. The T ratio, sin n i to sin r is called c the ref fractive index x of the 2nd medium m w.r.t. to 1st mediu um Refra active Ind dex ( ) The T ratio of speed s of light in air to the e speed in an ny medium is s called abso olute refractio on index. sin i By B Snell s law w 1 2 = i Air (i) sin r gure 1 fig By B definition Glas ss (ii) (air ) V Speed of light in Vacuum r 1 2 = Speed of f light in sec c ond medium m A An object in a denser me edium appears closer to the t surface when w viewed d from a rarer medium a shown in figure as f AB IB B , as B is class c to A OB AB A OA = , IA Re al depth d A AO = 1 2 = apparen nt depth A AI 1 2 = wh here O is object and I is its image. Principle of Reversibil R lity of Ligh ht: z The path of a ray of lig ght through a refracting surface s is rev versible P P Medi ium 1 i i 1 (a) r 70 Q 2 r 2 Q Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 04: Refraction at Plane Surface sin i sin r 1 2 = 1 2 2 1 = 71 2 1 and sin i sin r = 1 or sin r sin i 1 2 = = sin r sin i 1 2 1 Factors affecting Refractive Index of a medium: z Temperature: decreases with increase in temperature as speed of light in the medium increase with increase in temperature. z Nature of the medium: greater the optical density more is the value of . z Colour of light: As wavelength increases, decreases. Note: If the refractive indices of medium 1 and medium 2 are same, the speed of light will be same in both the media, so a ray of light will pass from medium 1 to medium 2 without any change in its direction even when the angle of incidence in medium 1 is not zero. z Conditions for no change in direction of light ray on refraction z A ray of light passes undeviated from medium 1 to medium 2 in either of the following two conditions: When the angle of incidence at the boundary of two media is zero (i.e., i = 0) When the refractive index of medium 2 is same as the refractive index medium 1. Refraction through a Glass Slab: AB incident ray, BC refracted ray, CD emergent ray. x lateral displacement The perpendicular distance between the emergent ray and the path of the incident ray is called lateral displacement. A N Lateral displacement depends on i B Thickness of glass slab (x t) Q P Refractive index of glass (x ) r Angle of incidence (x i) R 1 Wavelength of light (x ) S From the principle of reversibility i = e N C e D x E Multiple Image in a Thick Plane Glass z When an object is placed in front of a thick plane glass plate, a number of images are seen. z The second image is the brightest because light suffers strong reflection at the silvered surface. Applications of Refraction of Light: Note: To explain the applications use the concept, an object placed in denser medium when viewed from rarer medium appears nearer and vice versa. z Apparent bending of a stick under water. z A star appears twinkling in the sky. Volume 1 of 2 Universal Tutorials X ICSE Physics 71 72 z The sun is seen a fe ew minutes before it ris ses above the e horizon in n the morning and in the t evening fe ew minutes longer after its sets. z A coin ke ept in a ves ssel and no ot visible wh hen seen from m just below the edge of the vessel, can c be viewed d from the sa ame position n when water is powered into i the vess sel. z A print appears to be b raised wh hen seen from above thro ough a glass s block place ed on it. z A tank appears shallower than its actual depth h. Ap pparent bending of a stick k in ater wa Critic cal Angle: Criti ical angle is the angle of f incidence in n the denser r medium corresponding to which the e angle of refra action in the rarer medium m is 90 . Facto ors Affect ting Critic cal Angle e: Wavelength W ( (colour of light): As incr reases, critic cal angle dec creases. The T temperature: as temperature incr reases, decreases hence critical an ngle increase es. Note: : for violet colour is more in a mediu um hence cr ritical angle is s less for violet colour. Tota al Interna al Reflec ction: Whe en a ray of lig ght travelling g in a denser r medium is incident i at th he surface of f a rarer med dium such that the angle of o incidence e is greater than the cri itical angle for f the pair of media, the ray is refle ected back in nto the dense er medium. This T phenom menon is know wn as total in nternal reflec ction. C Condition fo or Total Internal Reflect tion: r Air Light should s travel from denser r to a rarer medium m The angle a of incidence must t be greater r than the r i c i critical angle for the e pair of med dia. Water Relat tion between refra active index and cr ritical ang gle: g a = sin ic g a = sin ic sin 90 a g = 1 = cosec ic sin i c ( sin 90 = 1) i Glass Air Appli ications of o Total Reflection R n: O On a hot sun nny day, the driver d of a ve ehicle may se ee a pond of o water on t the road befo ore him. It is s the phenom menon of mirage which is i often obse erved in dese erts. An A empty tes st tube placed inside wate er shines like e a mirror. A piece of dia amond spark kles when vie ewed from ce ertain directions. An A optical fib bre is used to transmit a light signa al over a long distance w with negligible loss in e energy. 72 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 04: Refraction at Plane Surface 73 Refraction through Prism: A prism is a transparent refracting medium bounded by two plane surfaces inclined at some angle. The plane surfaces through which the light passes are called the refracting surfaces or faces of the prism. REFRACTING The angle between the two refracting surfaces is called the angle of the prism. The line of intersection of the two surfaces is called the refracting edge of the prism. The section of the prism perpendicular to the refracting edge is called the principal section of prism. The angle between the path of incident ray in its direction and a path emergently opposite direction is called the angle of deviation, . In the given figure, AQN = ARN = 90 In AQN R, AQN + ARN = 180 A + N = 180 (1) In QN R, r1 + r2 + N = 180 (2) A = r1 + r2 (3) [From (1) and (2)] In DQR, is exterior angle i r1 + e r 2 = i + e (r1 + r2) = or i + e A = i.e. i + e = A + r1 r2 figure 1 figure 2 Factors affecting angle of deviation: z Material of prism: For a given angle of incidence, the prism with higher refractive index produces more deviation. z Angle of prism: As angle of prism increases angle of deviation increases. z Colour of light: Refractive index depends on wavelength. If wavelength is increased, refractive index decreases. Hence deviation decreases. eg. Violet light has smaller wavelength than red light. z Hence V > R. Therefore, violet light deviates more than red light. z Angle of Incidence: As angle of incidence Increases, angle of deviation decreases, reaches a minimum value and increases. The minimum value of angle of deviation is called angle of minimum deviation ( min) (see figure 2) z In minimum deviation position, angle of incidence (i) = angle of emergence (e) and r1 = r2. The refracted ray travels parallel to the base of the equilateral prism.(see figure 1) Note: In all cases the emergent ray bends towards the base of the prism. Volume 1 of 2 Universal Tutorials X ICSE Physics 73 74 Total Reflecting Prism: z A prism having an angle 90 between its two refracting surfaces and the other two angles each equal to 45 is called a total reflecting prism. It is used to: A deviate a ray of light through 90 45 Q deviate a ray of light through 180 P 45 erect the inverted image without deviation. i) Deviate a ray of light through 90 : P N 45 Q N 45 In the figure, ABC is a total reflecting prism. A beam of light is C B incident normally at the face AB. It passes undeviated into the prism and strikes at the face AC at an angle of incidence equal to 45 . For glass air interface, the critical angle is about 42 , therefore the beam of light suffers total internal reflection as the angle of incidence is greater than the critical angle. The beam then strikes the face BC, where it is incident normally and therefore passes undeviated. As a result the incident beam gets deviated through 90 while passing through the prism. This action of prism is used in a periscope where a total reflecting prism is used in place of a plane mirror. ii) Deviate a ray of light through 180 : In figure the beam of light from the object PQ falls B normally on the base AC of the prism, so it passes undeviated inside the prism and strikes the face AB of the prism travelling from glass to air at an angle of incidence 45 45 equal to 45 which is greater than the critical angle (42 for 45 45 glass air). C Therefore, the beam of light suffers total internal reflection A and strikes the face BC of the prism. At the face BC, the Q P P Q light rays travelling from glass to air at an angle of Object Image incidence equal to 45 , again suffer total internal reflection. The beam of light now falls normally on the face AC of the prism, and passes undeviated out of the prism forming the image P Q of the object PQ. The beam thus gets deviated by 180 . This action of prism is used in prism binoculars. iii) Erect the inverted image without deviation: 74 In figure the beam of light from the object PQ is incident parallel to the base of the prism and strikes the face AB of the prism. It suffers refraction from air to glass and strikes the face AC of the prism traveling from glass to air at an angle of incidence greater than the critical angle (= 42 ), therefore it suffers total internal reflection. B The beam now strikes the face BC of P the prism at an angle of incidence Q less than the critical angle hence it suffers refraction from glass to air and Q P bends away from the normal. 45 45 Object A C Image Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 04: Refraction at Plane Surface 75 The beam emerges parallel to the base. As a result of refraction, on emergence the rays are inverted. Such a prism is called the erecting prism. This action of prism is used in a slide projector. Total internal reflection and different prisms: Equilateral Prism A Q Incident ray 60 R Incident direction 60 60 60 S B C Emergent ray T 30 60 90 Prism A A 30 T A 30 A 30 30 P S 30 60 R P Q R R 30 60 Q S S 60 B 60 C B B P Q 60 C B (a) P Deviation through less than 60 D 30 60 60 C T Q 30 R C (b) No total internal reflection through 30 , 90 , 60 prism Total internal reflection through 30 , 90 , 60 prism Differences between total internal reflection and ordinary reflection Total internal reflection Ordinary reflection Takes place when ray travels from denser to rarer medium Takes place in any medium Takes place when i > Critical angle Takes place at any incidence angle 100% energy is transmitted There is a loss of energy REVIEW QUESTIONS: Direct questions: 1) What do you understand by refraction of light? 2) A ray of light is incident normally on a plane glass slab. What will be the angle of refraction and the angle of deviation for the ray? 3) What is the cause of refraction of light when it passes from one medium to another? 4) A ray of light passes from medium 1 to medium 2. Which of the following quantities of the refracted ray will differ from that of the incident ray: speed, intensity, frequency, wavelength? 5) State the Snell s laws of refraction. 6) Define absolute refractive index of a medium. 7) Define the term refractive index of a medium. What do you understand by the statement the refractive index of glass is 1.5 for white light ? Volume 1 of 2 Universal Tutorials X ICSE Physics 75 76 8) A light ray in passing p from water to a medium m (a) speeds s up (b b) slows dow wn. In each case, c give on ne example of o the medium m. 9) A monochromatic ray of light passes from air to glass. g The wavelength w o of light in air r is , the peed of light in air is c and a in glass is If the absolute a refra active index of glass is 1.5, write sp do own (a) the re elationship between b c an nd v, (b) the wavelength w o light in glas of ss. 10) Fo or which colo our of white li ight, is the re efractive inde ex of a transp parent mediu um the least? ? 11) Na ame two fact tors on which h the refractiv ve index of a medium de epends? Stat te how does it depend on n those factors. 12) What is the principle of rev versibility of the path of a light ray? he refractive index of wa ater with resp pect to air is s a w and of o glass with respect to air a is a g 13) Th Ex xpress the re efractive inde ex of glass with water. 14) Ex xplain the me eaning of the e term refraction. A ray of monochrom matic light is incident from m air on a gla ass slab. Dra aw a ray diag gram indicating the chang ge in its path h till it emerge es out of the slab. 15) In a robbery, a glass wind dow has bee en broken in nto tiny partic cles of glass s. Some of these t are fou und at the sc cene of the crime c and so ome in the thief s clothing g. If police ca an prove that t particles fou und from bot th the places s are identica al, they have a strong cas se. 16) A method of doing d so is to t suspend the t particles of glass in a special liq quid. Light of f a single co olour is pass sed through the liquid and a the parti icles are vie ewed through a microsc cope. The tem mperature of liquid is then slowly al ltered. This alters the sp peed of light t through liqu uid (i.e. it alt ters the refra active index) ). At a partic cular tempera ature, the pa articles of gl lass disappe ear. If this ha appens at the e same temp perature for both sets of f glass partic cles, they pro obably came e from the sa ame broken pane p of glass s. i) Why W is the lig ght used in the above me ethod, of sing gle colour? ii) When do the e particles of f glass disappear? 17) Ex xplain the following: When a lighted d candle is held h in front of o a thick pla ane glass mirror, several images can be seen, bu ut the second d image is the e brightest. 18) What is a prism m? With the help of diag gram of a prism, indicate e its refractin ng surfaces, refracting ed dge and base e. 19) Dr raw a diagram m to show th he refraction of a light ray y of single co olour through h a prism plac ced in the po osition of min nimum deviat tion. State ho ow is the ang gle of emerge ence related d angle of inc cidence. 20) What do you understand u b the deviat by tion produce ed by a prism m? State the e factors on which w the an ngle of deviat tion depends s. 21) Dr raw a curve showing the e variation in n the angle of deviation with the an ngle of incide ence at a pri ism surface. 22) Na ame the colo our of white light l which is s deviated (i) ) the most, (ii) the least, on passing through t a pri ism. 23) Th he diagram below b shows s two identic cal prisms A and B place ed wit th their face es parallel to o each other. A ray of light of single co olour PQ is incident at th he face of th he prism A. Complete th he dia agram to sh how the path h of the ray till it emerg ges out of th he pri ism B. 24) A student puts s his pencil in nto an empty y trough. What change will w be observ ved in the appearance of the pencil when w water is s poured into o the trough? The student ob bserves the pencil p throug gh water from m the positio on indicated in the e diagram. Na ame the phe enomenon which w accou unts for the above state ed ob bservation. Complete C the e diagram sh howing how the student t s ey ye sees the pencil p through water. 76 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 04: 0 Refraction n at Plane Su urface 77 25) An n object plac ced in one medium m whe en seen from m other med dium, appea ars shifted. Name N the fac ctors on whic ch the magnitude of shift depends an nd state how does it depe end on them. 26) Ex xplain the ter rm critical angle. 27) Na ame two fac ctors which affect a the cr ritical angle for a given pair of media. Stare ho ow do the fac ctors affect it t. 28) De efine the terms critical angle a and total internal reflection. r St tate two con nditions nece essary for tot tal internal re eflection to occur. o Write down d the rela ation for the critical angle e in terms of refractive ind dex. Draw diagrams to illustrate critic cal angle and d total interna al reflection. 29) What is a total reflecting pr rism 7. Draw w a diagram to o show one action a of the total reflecting prism. 30) Sh how with the e help of a diagram how a total reflecting prism can c be used d to turn a ra ay of light thr rough 90 . Name N one ins strument in which w such a prism is use ed. 31) What device other o than a plane mirror r, can be use ed to turn a ray of light th hrough 180 ? Draw a dia agram in sup pport of your answer. Nam me an instrument in whic ch this device e is used. 32) Th he diagram shows s two rig ght angled gl lass prisms (a) ( and (b). A ray of light is incident on each prism as sho own in the dia agram. Com mplete the path p of each h ray to sho ow how it en nters and em merges out of f the prism. (Critical ( angle for glass = 42 4 ) N NUMERICAL S: Class Work: W 1) Th he speed of light in air is s 3 108 m s 1. Calcula ate the spee ed of light in glass. The refractive [2 10 ind dex of glass is 1.5. 1 8 ms 1] 2) A monochrom matic ray of light strikes s the surfac ce of a transparent med dium at an angle of inc cidence 60 and gets re efracted into o the medium m at an ang gle of refract tion 45 . Wh hat is the [1.22] ref fractive index x of the medium? (sin 60 0 = 0866, sin n 45 = 0.707 7) 3) A coin is place ed at the bott tom of a bea aker containing water (re efractive inde ex = 4/3) to a depth of 12 [3 cm] 2 cm. By wha at height the coin appears s to be raised when seen n from vertica ally above? 4) A ray of light in ncident at an n angle 72 on o an equilat teral prism ge ets deviated through an angle 45 on [i2 = 33 ] n passing thro ough the pris sm. Calculate the angle of o emergence of the ray. 5) What should be b the angle of incidence e for a ray of light which suffer s a minimum deviati ion of 36 thr [48 ] rough an equ uilateral prism m? 6) Th he refractive index of wa ater with respect to air is s 4/3. What is the refrac ctive index of o air with [0.75] res spect to wate er? Home Work: W 1) Th he speed of light in diamond is 125,0 000 km s 1. What W is its re efractive inde ex? (Speed of light in 8 1 [2.4] air r 3 10 m s ) 2) A light ray enters a liquid at a an angle of incidence e 45 and it gets g refracte ed in liquid at t angle of ref [1.4] fraction 30 . Calculate th he refractive index i of the liquid. (G Given: sin 45 = 0.7, sin 30 3 = 0.5) 3) A ray of light of o wavelength h 5400 A suf ffers refractio on from air to o glass. Takin ng a w = 3 / 2 , find the wa [3600 8] avelength of light in glass s. 4) A ray of light incident at an angle 48 4 on a pris sm of refrac cting angle 60 suffers minimum [36 ] de eviation. Calc culate the an ngle of minim mum deviation n. 5) A postage stam mp kept belo ow a rectang gular glass block b of refractive index 1 1.5 when vie ewed from ve ertically above it, appears s to be raised d by 7.0 mm. . Calculate th he thickness of the glass block. [2.1 cm] 6) A water pond appears to be 2.7 m de eep. If the re efractive inde ex of water is 4/3, find the t actual de [3.6 m] epth of the po ond. Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 77 78 APPLICATION TYPE: T Class Work: W 1) Dr raw diagrams to show th he refraction n of light (i) air a to glass, (ii) glass to air. In each h diagram lab bel the incide ent ray, refra acted ray, the e angle of inc cidence (i) an nd the angle of refraction n (r). 2) A light ray pas sses from wa ater to i) air, ii) glass. In each case state, s how do oes the spee ed of light will change. 3) In the given dia agram, name e the ray whi ich represents the correc ct path of light while pass sing through h a glass bloc ck. 4) A ray of monochromatic green light enters a liquid from m air, as shown in fig. f The angle 1 is 45 an nd angle 2 is 30 Show in the t diagram the path of the ray afte er it strikes the t mirror and re en nters air. 5) Ho ow is the ang gle of emerg gence related d to the angle e of incidenc ce when prism is in the position p of mi inimum deviation? Illust trate your answer a with the help of o a labelled diagram using an eq quilateral pris sm. 6) A ray of light passes throu ugh an equilateral glass s prism such h that the ref fracted ray inside the pri ism is paralle el to its base e. How is the angle of emergence i2 re elated to the angle of inci idence i1. 7) An n object is viewed v throu ugh a glass prism with its vertex po ointing upwards. It appears to be dis splaced upward. Explain the reason. 8) A person stan nding on the edge of a swimming s po ool looks vertically down n at the tiles s on the bo ottom. He no otices that th he swimming g pool looks s shallower than t it really y is. Draw a diagram us sing at least two t rays to explain e the ob bservation. 9) A fish is lookin ng at a 1.0 m high plant at the edge e of the pond d. Will the plant appear shorter s or tal ller than its actual a height, , to the fish. Draw a ray diagram d to su upport your a answer. 10) In fig PQ and PR are the two light ray ys emerging from an obje ect P. The ra ay PQ is ref fracted as QS S. a) State the sp pecial name given g to the angle of incid dence z PQN N of the ray PQ Q. b) What is the angle of refr raction for the e refracted ra ay QS? c) Name the phenomenon p that occurs if the angle of incidence e PQN is inc creased. d) Draw in the diagram the e refracted ra ay for the inci ident ray PR and hence sh how the posit tion of image e of the objec ct P by the le etter P when seen vertica ally from abo ove. 11) A ray of light enters e a glass slab ABDC C as shown in i fig. and strikes at the ce entre O of the circular pa art AC of the e slab. The critical c angle of glass is 42 2 . Complete e the path of f the ray till it i emerges out o from the slab. Mark the e angles in th he diagram wherever w nec cessary. A 12) A ra ay of light passes p through a right angled pris sm as show wn in the adja acent diagram m. State the angles a of inc cidence at the faces AC and BC. Nam me the pheno omenon whic ch the ray suffers at the fa ace AC. 45 45 B 78 C Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 04: Refraction at Plane Surface 79 A 13) The diagram in Fig. shows a monochromatic ray of light OP, striking the face AB of an isosceles right-angled prism made of glass of critical angle 42 . P O a) Complete the diagram to show the path of the ray into and out of the prism, indicating the angles of incidence at each face of the prism. Hence write the angle of deviation of the ray OP. B C b) Draw a diagram to show the path if the incident ray OP is altered so that the angle OPB is 70 . c) Account for the difference in your answers to parts (a) and (b). 14) Fig. (i) and fig. (ii) show two glass prisms A and B Fig. (i) Incident rays are shown in the diagram. Trace the path of rays through the prism and as they emerge out. Fig. (ii) X 2x A 15) The fig. (v) along side shows a small object O at the bottom of a tank filled with a liquid whose critical angle is 45 . Three rays are drawn from O to the surface AB making angles of incidence to AB of 25 , 45 and 60 . Draw on the diagram the approximate path of each of these rays. B A B Fig. (v) O 16) A narrow parallel beam of light from a ray box at D is directed to the centre O of a circle, of which the semi circular glass block is a part. fig. (vii) E Narrow beam F i) Why is the beam not refracted when it enters the glass at E, from ray box yet is noticeably deviated when it leaves the block at O? Fig. (vii) By making suitable measurements, find: ii) The angle of incidence when the beam strikes O. iii) The angle of refraction when the light reenters the air. O 17) a) Write down an expression for a g in terms of the angle i and r. b) If angle r = 90 what is the corresponding angle i called? c) What is the physical significance of the angle i in part (b)? 18) A monochromatic point source of light O is seen through a rectangular O glass block PQRS. Paths of two rays, in and outside the block, are shown in the figure below. P Q i) Does the source O appear to be nearer or farther with respect to the surface PQ. S R ii) How does the shift depend on the thickness PS or QR of the block? iii) Justify your answer in (ii) with the help of an appropriate ray diagram. iv) For the same rectangular glass block, which colour from the visible spectra will produce the maximum shift? 1 Air 19) A ray of monochromatic green light enters a liquid from air, as shown in figure. The angle 1 is 45 and angle 2 is 30 . Show in the diagram the 2 Water path of the ray after it strikes the mirror and re enters air. Calculate the refractive index of the liquid. (Given: sin 45 = 0.7, sin 30 = 0.5) Plane mirror Volume 1 of 2 Universal Tutorials X ICSE Physics 79 80 Home Work: W 1) Ho ow is the refr ractive index x of a medium m related to the t speed of light in it? 2) A ray of light passes p from air to water. In Fig. which of the ray A, A B, C an nd D is the co orrect refract ted ray? 3) A ray of light strikes s the su urface of a re ectangular glass g block such that the angle of inc cidence is (i) 0 (ii) 42 . In n each case, draw diagra am to show the t path take en by the ray y as it passes through the e glass block k and emerge es from it. 4) Ho ow does the angle of de eviation prod duced by a prism p change e with increa ase in (i) the e angle of inc cidence, (ii) the t waveleng gth of inciden nt light and iii) the refracting angle of prism ? 5) A ray of light of o single colour is incide ent on an equilateral glas ss prism placed in the position p of mi inimum devia ation. Draw a ray diagram m to show th he path of the e light ray till l it emerges out of the pri ism. 6) A light ray of yellow colou ur is incident on an equ uilateral glass prism at a an angle of incidence eq qual to 48 and a suffers minimum m de eviation by an a angle of 36 . 3 (i) What will be the e angle of em mergence? (i ii) If the angl le of incidence is change ed to (a) 30 , (b) 60 , sta ate whether the angle of deviation will be equal to o, less than or o more than 36 ? 7) Water in a pon nd appears to t be only th hree quarters s of its actua al depth. Wh hat property of light is res sponsible for r this observa ation? Illustrate your ans swer with the e help of a ray y diagram. 8) Dr raw a ray dia agram to show the appe earance a st tick partially immersed in n water. Exp plain your an nswer. 9) Th he diagram in n fig shows a point sourc ce P inside a water cont tainer. Th hree rays A, B and C st tarting from P are shown up to the water su urface. Show w in the diagra am the path of these ray ys after strikin ng the wa ater surface. The critical angle a for water air surface is 40 . 10) Th he refractive index of gla ass is 1.5. Fr rom a point P inside a glass block, d draw rays PA A, PB and PC C incident on n the glass-a air surface at a an angle of o incidence 30 , 42 and 60 respec ctively. In the e diagram sh how the appr roximate dire ection of thes se rays as th hey emerge o out of the blo ock. What is the angle of refraction fo or the ray PB? [Take sin 42 4 = 2/3] 11) In fig a ray of light l PQ is in ncident norm mally on the fa ace AB of an n equilateral gla ass prism. Complete C the e ray diagra am showing its emergence into air aft ter passing through t the prism. p Write the angles of o incidence at the faces AB B and AC of f the prism. Name the phenomenon n which the ray of light su uffers at the face f AB, AC and BC of th he prism. 12) F (iii) Fig. A B Fig. (iv) Copy fig. (iii) and fig. (iv v) and complete it to show w the rays emerg ging out of th he prism B. S State the prin nciples used for co ompleting the e diagram. 13) A ray of light enters e a glas ss slab ABC CD as shown n in fig. (vi i). the critical angle of gla ass is 42 . Copy C the figu ure and B co omplete the path p till it eme erges from th he slab. A B 30 Fig. (vi) D C 14) Dr raw diagrams showing th he transmiss sion of light from a dens ser medium to a rarer medium m at dif fferent angles of incidenc ce such as (i) ) i < ic (ii) i = ic (iii) i > ic. Where ic is critical angle e. 80 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 04: 0 Refraction n at Plane Su urface 81 15) In the diagram, AO is a ray y of light incid dent on a rec ctangular gla ass block. A a) Complete th he path of th he ray through the block. b) In the diag gram, mark the angle of incidence (i) and th he angle of f O refraction (r) at the firs st interface. How is the refractive ind dex of glass s related to th he angles i and a r? c) Mark angle of emergence by the letter e. How are the angles s i and e rela ated? d) Which two rays are para allel to each other? Name them. e) Indicate in the diagram m the lateral displacemen d nt between th he emergent t ray and the e incident ray. A B P 16) Th he diagram below b shows s two prisms A and B. A ray of light of single colou ur PQ is inc cident at the e face of the e prism A. Q Co omplete the diagram to o show the path of the e ray till it em merges out of o the prism B. B MIS SCELLANEO OUS: 1) A lig ght ray suffe ers reflection and refraction at the bo oundary in passing p from m air to water. Draw a neat labelled dia agram to sho ow it. 2) Whe en a ray of lig ght from air enters e a denser medium, , it: a) bends b away from f the nor rmal b) bends towar rds the norma al d) is reflected back c) goes g undevia ated b 3) Which of the following has th he highest re efractive inde ex d) R a) Glass b) Water c) Diamond D Ruby. 4) If a light ray do oes not und dergo refraction at the boundary be etween two media, the angle of incid dence is c) 60 d) 9 a) 0 b) 45 6 90 . 5) For which colour of white ligh ht, is the refr ractive index of glass the most? 6) A ra ay of light in passing p from m a transpare ent medium 1 to another transparent t m medium 2 i) speeds s up, ii) slows s down. In each case e, state whet ther the refra active index of o medium 2 is equal to, less than o greater tha or an the refrac ctive index of f medium 1. 4 3 7) The e refractive index of water and glas ss with resp pect to air are a and respectiv vely. The 3 2 refra active index of water with h respect to glass g will be: : 4 3 4 3 4 3 3 4 a) b) + c) d) 3 2 3 2 3 2 2 3 8) Stat te and explai in the laws of o refraction. Describe an experiment to verify the laws. 9) In th he adjacent diagram, d AO is a ray of light incident on a rectang gular glass bl lock. a) Complete C the e path of the ray through the block. b) In the diagram, mark the angle of inc cidence (i) an nd the angle of refraction n (r) at t first interf the face. How is the refractiv ve index of gl lass related to t the angles s i and r I r? c) Mark M angle of o emergence e by the lette er e. How are e the angles i and e relate ed? d) Which W two ra ays are parallel to each other? Name them. e) Indicate in th he diagram the t lateral displacement d t between th he emergent ray and the e incident r ray. 10) Fill in i the blanks s to complete e the followin ng sentences s: a) When W light travels from a rarer to a de enser medium, it bends_ ___________ _________ b) When W light travels from a denser to a rarer medium, it bends ___________ _ _________ Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 81 82 c) The refractive index of glass with respect to air is 3/2. The refractive index of air with respect to glass will be _________________________________ 11) In the diagram below, label the incident, refracted and emergent rays. Also indicate the angle of deviation. 12) Define the term angle of deviation. 13) State whether the following statement is true or false The deviation produced by a prism is independent of the angle of incidence and is same for all the colours of light. 14) Complete the following sentence Angle of deviation is the angle which the ray makes with the direction of ray . 15) The deviation produced by an equilateral Prism when a ray of light is incident on it, does not depend on: a) angle of incidence b) colour of light c) material of prism d) size of prism. 16) Which of the two prisms A made of crown glass and B made of flint glass deviates a ray of light more? 17) How does the angle of deviation depend on the angle of the prism? 18) A ray of light is normally incident on one face of an equilateral glass prism. Answer the following: a) What is the angle of incidence on the first face of the prism? b) What is the angle of refraction from the first face of the prism? c) What will be the angle of incidence at the second face of the prism? d) Will the light ray suffer minimum deviation by the prism? 19) How is the refractive index of a medium related to the real and apparent depths of an object in that medium? 20) Draw a properly labeled ray diagram to show that the apparent depth of water in a tank is less than its real depth. How is the refractive index of water calculated from its real and apparent depths? Re al depth 21) Prove that Refractive index = Apparent depth 22) What causes the twinkling of stars? 23) A fish swimming in a pond seems nearer to the surface than it really is. Give the reason. 24) During sunset and sunrise, the sun is seen even when it is slightly below the horizon. Name the phenomenon responsible for it. 25) How is the critical angle related to the refractive index of a medium? 26) State the approximate value of the critical angle for glass air surface. 27) What is mean by the statement the critical angle for diamond is 24 ? 28) A light ray is incident from a denser medium on the boundary separating it from a rarer medium at an angle of incidence equal to the critical angle. What is the angle of refraction for the ray? 29) The critical angle for glass air interface is 45 for the light of yellow colour. State whether it will be less than, equal to, or more than 45 for (i) red light, (ii) blue light 30) Fill in the blanks to complete the following sentences: a) Total internal reflection occurs when a ray of light passes from a _____ medium to a medium. b) Critical angle is the angle of ______ in denser medium for which the angle of _______ in rarer medium is ________ 31) Total internal reflection occurs when a) No light is allowed to enter or leave a medium b) the light travels from a rarer to a denser medium at an angle of incidence greater than the critical angle c) the light travels from a denser to a rater medium 82 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 04: 0 Refraction n at Plane Su urface 32) 33) 34) 35) 36) 37) 38) 39) 83 d) t the light trav vels from a denser d to a rarer mediu um at an ang gle of incide ence greater r than the c critical angle. Stat te whether th he following statement is s true or false e: If the angl le of incidence is greater r than the critic cal angle, lig ght is not ref fracted at all, when it falls on the surface from a denser med dium to a rare er medium. Stat te three actio ons that a tot tal reflecting prism can pr roduce. Men ntion one diff ference betw ween reflectio on of light fr rom a plane mirror and to otal internal reflection of lig ght from a pr rism. Stat te one advan ntage of using a total refle ecting prism as a reflecto or in place of f a plane mirr ror. Draw w a neat lab beled ray diagram to sh how the tota al internal ref flection of a ray of light normally incid dent on one face of a 30 , 90 , 60 pr rism Two o isosceles right r angled glass prisms s are placed d near each other as show wn in fig. Co omplete the path p of the lig ght ray enter ring the first prism till it em merges out of o the second d prism. Wha at is mirage in i a desert? Name the ph henomenon for its cause. The e surface of an a empty tes st tube kept in a beaker of o water shines like a mirr ror. Name the e phenomen non responsib ble for it. PREVIOUS S BOARD QU UESTIONS: 1) i) Define the term refracti ive index of a medium in n terms of ve elocity of light t. ii) A ray of lig ght moves from f a rarer medium to a denser medium as s shown in the adjacent diagram. Write W down the number r of ray which represents s the partially y reflected ray. [2012] 2) A ray of light in ncident at an n angle of incidence i pa asses through h an equilate eral glass prism such tha at the refracted ray insid de the prism is parallel to o its base an nd emerges from the pris sm at an an ngle of emerg gence e. i) How is the angle of eme ergence e re elated to the angle a of incid dence i ? ii) What can you y say abou ut the value of o angle of de eviation in su uch a situatio on? 3) i) What is me [2012] eant by the te erm critical angle? ii) How is it related to the refractive r ind dex of the me edium? iii) Does the depth d of a tank t of wate er appear to o change or r remain the e same when viewed [2012] normally fro om above? 4) A ray of light PQ P is inciden nt normally on o the hypote enuse of an n isoceles right r angled prism ABC C as shown n in the [2012] ad djacent diagra am. i) Copy the diagram and complete the e path of the e ray PQ till it emerge es from the prism. p ii) What is the e value of the e angle of deviation of the e ray? iii) Name an instrument where w this ac ction of the prism is used. 5) In the diagram below, PQ is a ray of lig ght incident on o a rectangu ular glass blo ock. P Q i) Copy the di iagram and complete c the e path of the ray of light th hrough the g glass block. In yo our diagram, mark the angle of incidence by letter r i' and the a angle of emergen nce by the let tter e . ii) How are the [2011] e angles i' and a e related d to each oth her? Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 83 84 6) A ray of monochromatic light enters a liquid from air as 45 Air shown in the diagram given below: i) Copy the diagram and show in the diagram the path of Liquid Plane mirror the ray of light after it strikes the mirror and re enters the 30 medium of air. ii) Mark in your diagram the two angles on the surface of separation when the ray of light moves out from the liquid to air. [2011] 7) i) State the laws of refraction of light. ii) Write a relation between the angle of incidence (i), angle of emergence (e), angle of prism (A) and angle of deviation (d) for a ray of light passing through an equilateral prism. [2011] 8) An object is placed in front of a lens between its optical centre and the focus and forms a virtual, erect and diminished image. [2011] i) Name the lens which formed this image. ii) Draw a ray diagram to show the formation of the image with the above stated characteristics. 9) A ray of light strikes the surface of a rectangular glass block such that the angle of incidence is (i) 0 (ii) 42 . Sketch a diagram to show the approximate path taken by the ray in each case as it passes through the glass block and emerges from it. (2009) 10) State the conditions required for total internal reflection of light to take place (2009) 11) How does the value of angle of deviation produced by a prism change with an increase in the: i) Value of angle of incidence ii) wavelength of incident light? (2009) 12) A monochromative beam of light of wavelength passes from air into a glass block. Write an expression to show the relation between the speed of light in air and the speed of light in glass. (2008) 13) As the ray of light passes from air to glass, state how the wavelength of light changes. Does it increase, decrease or remain constant? (2008) 14) Two isosceles right angled glass prisms are placed near each other as shown in the figure. Complete the path of the light ray entering the first isosceles right angled glass prism till it emerges from the second identical prism. (2008) 15) Draw a labeled ray diagram to illustrate i) Critical angle (2) total internal reflection, for a ray of light moving from one medium to another ii) Write a formula to express the relationship between refractive index of the denser medium with respect to rarer medium and its critical angle for that pair of media (2008) 16) The diagram below shows ray of light incident on an equilateral glass prism placed in minimum deviation position. (2008) Copy the diagram and complete it to show the path of the refracted ray and the emergent ray. 17) How are angle of incidence and angle of emergence related to each other in this position of the prism? 18) State Snell s law of refraction of light (2007) 19) Mention one difference between reflection of light from a plane mirror and total internal reflection of light from a prism. (2007) 20) How does the speed of light in glass change on increasing the wavelength of light? (2007) 21) With the help of a well labeled diagram show that the apparent depth of an object such as a coin in water is less than its real depth. (2007) 22) How is the refractive index of water related to the real depth and the apparent depth of a column of water? (2007) 84 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 04: 0 Refraction n at Plane Su urface 85 23) PQ Q and PR are e two light ra ays emerging g from the ob bject P as shown in the fig gure below: (2006) a) What is the e special nam me given to the angle of incidence i ( PQN) N1 of ray PQ? Air R Q b) Copy the ra ay diagram and a complete e it to show the t position of the image of the object P when w seen ob bliquely from above. Water c) Name the phenomeno on that occu urs if the an ngle of incid dence N P PQN is in ncreased still further. 24) i) State Snell l s law. ii) Calculate th he velocity of o the light in a glass bloc ck of refractiv ve index 1.5 (velocity of light l in air = 3 108 ms m 1) 25) Th he velocity of f light in diam mond is 121,000 kms 1. What is its refractive r ind dex? (Velocit ty of light 8 in air is 3 10 m/s). 26) a) A monochr romatic point t source of light O is se een through a rectangula ar glass block ABCD. Paths of tw wo rays, in and a outside the t block, ar re shown in the O figure along gside. i) Does th he source O O appear to o be nearer or farther with w B A respect to the surfac ce AD? ii) How does the shift depend on the t thickness s (AD or BC) of D C the block? iii) Justify your y answer in (ii) with the help of an appropriate ray diagram m. iv) For the same rectan ngular glass block, which colour from m the visible e spectra will produce the max ximum shift? b) A postage stamp appea ars raised by y 7.0 mm wh hen placed under u a recta angular glass s block of refractive in ndex 1.5. Fin nd the thickne ess of the gla ass block. A P 27) i) In the diagr ram alongsid de, a ray of light PQ is inc cident norma ally Q on one fac ce AB of an equilateral glass prism. . What are the t angles of in ncidence at th he faces AB and AC? ii) Complete the ray diagr ram showing g its emergen nce into air after a 6 60 B C passing through the pris sm. 28) Dr raw a ray dia agram to illus strate the ben nding of a sti ick in water. 29) Th he diagram alongside a shows the path h of a ray of f light through a rectangular r g glass block placed p in a liq quid of unifor rm density. Liquid i) Does the lig ght speed up p or slow dow wn in glass? Glass i Liquid ii) Give reason ns for your answer. a r iii) What is the e angular de eviation of th he emergent ray from the e glass block k with respect to the incident ray? iv) ) Show with the help of ray diagram m, the path of o the ray wh hen incident t normally on n the first surface of the t glass block, through the t block and d the liquid. P1 P2 30) Tw wo isosceles s right-angle ed prisms ar re arranged as shown in the fig gure. i) Copy the diagram d and d complete the t path of the ray AB along which it pas sses through h the prisms and a comes out. o ii) Name the phenomenon p n being displa ayed by the path p of the ra ay in the diag gram. 31) Water in a pon nd appears to o be only thre ee quarters of o its actual depth. d a) i) What pr roperty of ligh ht is respons sible for this observation? o ?] ii) Illustrate e your answe er with the he elp of a ray diagram. d b) i) The critical angle for the glass of o which the equilateral prism p ABC is made e, is 48 . A ra ay of light inc cident on the e side AB of f the prism is refrac cted along DE D such that t the angle it t makes with h the side AC is 13 38 . Also, E EDB = 90 . Copy C the diag gram. Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 85 86 32) 33) 34) 35) 36) 37) 38) 1) Draw the path of the ray incident on the side AB. (Which travels along DE.) 2) Show the path along which the ray DE travels from the point E onwards and through the side BC. ii) Which two conditions must be fulfilled for total internal reflection of light to occur? i) What is meant by refraction? ii) Express the refractive index p of a medium: a) in terms of the velocity of light; b) in terms of the angle of incidence i in air and the angle of refraction r in a denser medium. iii) If a ray of light passes from medium I to medium II without any change of direction, what can be said about the refractive indices of these media (angle i is not 0)? i) Define critical angle. ii) A ray of light passes through a right angled prism as shown in the figure. State the angles of incidence at the faces AC and BC. i) What is an optical fibre? ii) Give one practical use of an optical fibre. i) If a monochromatic beam of light, undergoes minimum deviation through an equiangular prism, how does the beam pass through the prism, with respect to its base? ii) If white light is used in the same way as in (i) above, what change is expected in the emergent beam? State two advantages of using a right angled prism as a reflector, rather than a plane mirror. A prism deviates a monochromatic ray of light through an angle when the angle of incidence at the surface of the prism is i . i) Draw a graph showing the variation of with i . On Your graph show the angle of minimum deviation. ii) What is the relation between the angle of incidence and the angle of emergence when the ray suffers minimum deviation? Draw a ray diagram to illustrate how a ray of light incident obliquely on one face of a rectangular glass slab of uniform thickness emerges parallel to its original direction. Mention which pairs of angles are equal? ANSWERS: Previous Board Questions: 1) i) Refractive index of a medium = Speed of light in air Speed of light in medium ii) Ray 2. 2) i) e = i ii) Angle of deviation is minimum. 3) i) Critical angle is the angle of incidence of a ray of light in a denser medium for which the angle of refraction in air (or rarer medium) is 90 . ii) sin ic = 1 or critical angle ic = sin 1 1 iii) Appear to change (decrease). 4) i) The completed diagram is shown ii) Angle of deviation = 180 . iii) Prism binocular. 86 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 04: 0 Refraction n at Plane Su urface 87 i = 42 i = 0 9) (i) (ii) Glas ss 10) i) Light L must e going from denser d to rat ter medium. ii) Angle of incidence in denser medium m must be greater than cr ritical angle. 11) i) with w increase in angle of o incidence, angle of de eviation first decreases an nd then increases ii) Lesser the wavelength, w m more will be deviation. 42 c) Total interna al reflection 23) a) Critical angle 24) i) The ratio of f sine of angl le of incidenc ce to the sine e of angle of f refraction is s constant. 26) sin s i = sin r s 3 10 8 3 10 1 8 1.5 = or v2 = v2 = 2 108 m/s m 1 v2 1.5 Sp peed of light in diamond = 121, 000 km/s = 121 106 m/s Sp peed of light t in air 3 108 Refractive in ndex of diam mond = = = 2.48 Spee ed of light in diamond 121 106 a) i) The sou urce O appe ears to be ne earer with res spect to the surface AB. ii) The shif ft increases with increas se in the thic ckness of the glass slab. iii) See figu ure. iv) Violet co olour light will produce maximum shift ft. ii) We know th hat 25) i v1 1 = v2 2 b) Refractive index i = Re al depth App parent depth The refract tive index of the glass bl lock is give 1.5, postage e stamp appears rai ised by 7 mm m. Let the thickness of the e glass block k be x. Then, 1.5 = x x 7 1.5 (x 7) 7 = x Or 1.5 1 x = 10.5 = x x= 27) Or 0.5 x = 10.5 10 .5 = 21 mm 0 .5 i) of inciden nce at face AB A = 0 of inciden nce at face AC A = 60 ii) See figure 28) Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 87 88 29) Since the speed of light t in liquid = Speed of light l in air 3 108 = R Refractive ind dex of liquid Refractive index of liquid i) Since the refractive r ind dex of glass is usually higher h than that t of liquid, hence the speed of light in glas ss will be less s. Since there e is no refraction of light t at the boun ndaries of th he glass bloc ck, it is poss sible only when the sp peed of light through the liquid as we ell as through h the block is s the same. Hence H the ratio betwe een the spe eed of light through the liquid to th he speed of f light through gla ass must be 1 (one). As shown by b dotted lin ne in the dia agram, the emergent ray y is parallel t to the incident ray y (when prod duced) and so o there is no o angular dev viation. The speed of light, trave elling from liq quid to glass s; slows down n. 30) Se ee diagram alongside. a Th he phenomen non of total in nternal reflec ction takes place p in both the pri isms. 31) a) i) The pon nd appears to be three quarters q of its s actual dep pth due to pro operty of ref fraction of light. Refractive index i = Since = Re al Depth Ap pparent Dept th 4 for water 3 Apparent Depth = 48 3 Real dept th 4 Q.19 32) he ray HD th hrough prism m is normal to AB, i.e. i = 0 , hen nce angle i which w HD b) 1) Since th makes with w normal to t AB must also be 0 . Hence H light will w travel alo ong HD norm mal to AB before striking s face AC. A 2) Since, DEN = DE EC NEC; DEN = 138 90 = 48 8 Which is s equal to cr ritical angle. Hence angle e of refraction LNEC mus st be 90 , i.e e., the ray will go to owards ECF. ii) Condition ns for total in nternal reflection are: 1) The ray must pass fr rom denser to t rarer medi ium. 2) Angle of f incidence must m be greater than the critical angle e. i) It is a phen nomenon in which w a ray of o light devia ates from its original path h, while trave elling from one optical medium to another a optic cal medium. ii) a) The refr ractive index ii of an optical medium is defined as the ratio be etween the velocity v of light in vacuum v divid ded by the ve elocity of light in the given n optical med dium. Thus, = Velocity y of light in va acuum Velocity of light in the given optical o mediu um b) If light tr ravels from air a into another denser me edium, the re efractive inde ex n of the medium. m = 88 Sine of o the angle of o incidence in i air Sine of the angle of refract tionin the denser medium m Universal Tu utorials X IC CSE Physics s i.e., = sin i sin r Volu ume 1 of 2 Chapter 04: 0 Refraction n at Plane Su urface 33) 89 iii) When a ray y of light trav vels from me edium I to medium m II with hout any cha ange of direc ction, it is possible un nder either of f the following two conditions: a) A ray of light is incident normally y on the surfa ace separatin ng two media a. b) The refr ractive index of medium I is equal to the t refractive e index of me edium II. i) The critical angle is the angle of inc cidence in the e denser me edium correspond ding to which h the angle of o refraction in a rarer me edium is 90 . ce is 45 and d at BC ang gle of inciden nce is ii) At AC angle of incidenc 0 . 34) 35) 36) 37) i) It s device used u to trans smit light signals from on ne place to another witho out appreciab ble loss of energy, use es the pheno omenon of to otal internal re eflection. ii) tele communication. i) It is parallel l to the base of the prism m. ii) It splits into i its seven n component t colours: (VI IBGYOR). i) The image is not blurred d and is mor re sharp. ii) In case of plane mirror r, some mois sture or dust t particles if present; do not let produce clear and distinct t image. i) Required graph is show wn in following figure: ii) The angle o of incidence = the angle of o emergenc ce, when the ra ay suffers a minimum m dev viation. 38) i=e r1 = r2 r1 r2 Rectangular glass slab See the diagram alongside a in which w rays o of incidence, refracted ray an nd emergent t rays for re ectangular glass slab ar re drawn. Inciden nt ray and emergent ray y are parallel and so the e angle of inciden nce i and ang gle of emerge ence are equ ual. Emergent ray Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 89 90 Chapter 05: Refraction through a Lens Chapter Map: Refraction through a Lens Types of Lens Convex Lens Concave Lens Action of lens as a set of Prisms Imp. Definitions Ray Diagrams Convex lens Concave lens Power of lens Eye limitations Simple Microscope Determination of focal length Distant object method Auxillary plane Mirror method Uses of lenses Refraction through a lens: A lens is a transparent refracting medium bound by two surfaces of which at least one surface is spherical. Types of Lenses: Convex Lenses (converging lens): z A lens which is thick in the middle and thinner at its edges is called convex lens. z Types: i) biconvex ii) Plano convex iii) Concavo convex Concave Lens (diverging lens): z A lens which is thicker at the edges and thinner in the middle is called a concave lens. 90 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 05: 0 Refraction n through a Lens L 91 z Types: a) ) Biconcave b) Plano co oncave c) Co onvexo conc cave Actio on of Le ens as a Prism: A le ens can be co onsidered as s being made e up of a set of prisms as s shown in fig gure. But for conven nience the refraction r of f light through a lens can be understood by considering c a lens as being made up u of a rect tangular bloc ck at the cent tre and two (or ( more) pris sms on eithe er side of it. As light l ray strikes the tiny prism, the ray bends to owards the base b of thes se prisms. Impo ortant De efinition ns: Cen ntre of curva ature: The centre c of the e sphere of which w the len ns is a part is called the centre of curv vature of that t surface of lens. 1 2 Princ cipal 1 2 Principal Ax xis C2 C1 Optica al Centr re (a) Convex Le ens Axis C1 C2 Optical Centre (b) Concave Lens Rad dius of curva ature: The radius of the surface of which w the lens s forms a pa art, is called the t radius of curvature of th hat surface of o lens. Prin ncipal axis: It is the line joining the centres c of curvature of the two surfaces s of the lens. Opt tical centre: It is a point t on the prin ncipal axis of f the lens such h that a ray y of light passing though this point emerges para allel to its dire ection of inci idence. Note: : For a thin le ens ray pass ses undeviate ed through optic o centre. Prin nciple foci: Light can pass p through h a lens from m either dire ection. There efore, a lens s has two principal foci wh hich are situa ated at equa al distances from the opt tical center, one on eithe er side of the lens. These are known as a the first fo ocal point (or first focus) F1 and the s second focal point (or seco ond focus) F2. Firs st focal poin nt: For a con nvex lens, th he first focal point is a po oint F1 on the e principal axis a of the lens s such that th he rays of lig ght starting fr rom it, after refraction r thr rough the len ns, become parallel p to the principal axis s of the lens s. For a conc cave lens, firs st focal point t is a point F1 on the prin ncipal axis of th he lens such that the rays of light app pearing to meet at it, afte er refraction f from the lens s become para allel to the pr rincipal axis of o the lens. Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 91 92 Firs st focal leng gth: The distance from the t optical centre c of the first focal p point is called d the first foca al length f1 of f the lens. Firs st focal plan ne: A plane passing p throu ugh the first focal point and a normal t to the princip pal axis is calle ed the first fo ocal plane. Sec cond focal point: p For a convex c lens, the second focal point is s a point F2 o on the princip pal axis of the lens such th hat the rays of o light incide ent parallel to t the princip pal axis of the lens after refraction from m the lens pa ass through this point. Sec cond focal le ength: The distance d from m the optical l centre to th he second fo ocal point is called c the seco ond focal len ngth of the lens. Sec cond focal plane: p A plan ne passing through the second s focal l point and n normal to the e principal axis s is called the e second foc cal plane. Ray Diagram ms: Princ cipal Rays s in constructing Ray R diagr ram: A ray of light incident at the optical ce entre O passes undeviate ed through th he lens A ray of light incident par rallel to the principal p axis of the lens after a refractio on passes through the s second focus s F2 (in a co onvex lens) or appears to t diverge th hrough the s second focus s F2 (in a c concave lens s) as shown. A ray of light t incident thr rough the firs st focus F1 (in a convex lens) or appearing to me eet at first f focus F1 (in a concave len ns) emerges s parallel to th he principal axis a after ref fraction. 92 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 05: 0 Refraction n through a Lens L 93 Convex Lens s: a) Object O at infinity i (i.e e. a very distant d obj ject): z The light rays from any a point of such object t can be tre eated as para allel. C Characterist tics of the im mage forme ed: The im mage is at the e focus on th he other side e of the lens. It is (a) ( real (b) inverted and d (c) highly diminishe ed. (a a) U Use: Lens is s used as a camera c lens and a burnin ng glass. In a ca amera, the object lies ver ry far (effecti ively at infinity) from the lens and the e image is formed d at the film which w is at th he second focus (or in se econd focal p plane). When used as a burning glass, the rays fro om the sun (at infinity) ar re brought to o focus on a piece e of paper ke ept in the foc cal plane of the lens. Due e to sufficient t heat of the sun rays, the paper burns. b) Object O bey yond 2F: C Characterist tics of the im mage forme ed: The im mage is betw ween F2, and 2F2 on the other o side of f the lens. It t is (a) real (b) ( inverted, and (c) dim minished. U Use: In a ca amera lens, when w the object, not very y far, is to be photographe ed c) Object O at 2F: 2 C Characterist tics of the im mage forme ed: The im mage is at 2F2 on the other side of the len ns. It is (a) re eal (b) inverted, and (c) of the same size as s the object. d) Object O bet tween F and 2F: C Characterist tics of the im mage forme ed: The im mage is beyo ond 2F2 on th he other side of the lens. It is (a a) real (b) in nverted, and (c) magnified. U Use: This ty ype of image e formation is s used in cin nema and slide projectors s. Here the magnified m image is obtained on o the scree en placed at a distance. Note: : Care must t be taken to o put the slid de or the film m (i.e. objec ct) upside do own since a real and inverted im mage is forme ed in this cas se. Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 93 94 e) Object O at F: F C Characterist tics of the im mage forme ed The im mage is at inf finity on the other o side of f the lens. It is (a) real, , (b) inverted d and (c) hig ghly magnif fied. The ar rrangement is used to obtain o a parallel beam of light by placing p the bulb b at the fo ocus of conv vex lens. f) Object O betw ween the lens and F (between 0 and F) ): Characterist C tics of the im mage forme ed The im mage is on th he side of th he object beh hind it. It is (a) virtua al (b) erect or upright and (c) magnified. In this case the ra ays after ref fraction beco ome diverge ent, therefo ore, they meet only when w produc ced backwa ards. This gives g a vir rtual image. U Use: This ty ype of image e formation is used while e using a co onvex lens as a reading lens or a magnif fying glass of o a simple microscope. m Here H a magn nified image of a tiny obj ject (such as lette ers) is forme ed. The eye sees s it distinc ctly by formin ng a real ima age on the re etina. Concave Len ns: z When the e object is at a infinity: Let L a beam of o parallel rays coming from an object place ed at infinity y fall on a thin conca ave lens L. After A refractio on through th he lens L, the rays diverge and d on being produced p ba ackwards, they meet at A in the e second foc cal plane at F2 i.e. to the observer on the e other side e of object, the rays appear to o diverge from A . The erefore, for an a object placed at t infinity, the e image form med by the concave lens is situated in the focal plane of o the lens and on the side of ob bject. Cha aracteristics of the image: z The imag ge is at F2 on n the side of o the object. It is (a) virt tual, (b) erec ct, and (c) very much diminished. z When the e object is between in nfinity and the optical centre of the e concave lens: Let AB B be an uprigh ht object placed p at a point on the principal axis betwee en the optical centre and infinity, in nfront of a concave c lens s. Two rays AP and AO leaving the e point A of o object, after a refraction through the lens, dive erge from each e other. The e ray AP inci ident parallel to the princ cipal axis is ref fracted as PQ Q which appe ears to come e from the se econd focus F2. z The ray AO, A incident through t the optical o centre e 0 passes undeviated u a after refractio on as OM. These ray ys PQ and OM do not meet at any point. But t the refracte ed ray PQ, on being produced backwards, meets the ra ay AOM at a point A which is the ima age of A. Thus A B is the virtual l image of AB B. 94 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 05: Refraction through a Lens 95 Characteristics of the image: z The image is between the lens and focus on the side of object. It is (a) virtual, (b) erect and (c) diminished. z Thus, irrespective of the position of the object, the image formed by a thin concave (or divergent) lens is always virtual, upright, diminished and it is situated between the focus F2 and the lens. z As the object is gradually moved towards the lens, the image also shifts towards the optical centre of lens and the size of image gradually increases, but it remains always smaller than the size of object. If the object is at a distance equal to the focal length of lens, the image is exactly at the mid-point between the optical centre and the second focus of lens. z Difference between a convex and a concave lens Convex lens Concave lens It is thick in the middle and thin at its It is thin in the middle and thick at its edges. edges. It converges the incident rays towards the It diverges the incident rays away from the principal axis. principal axis It has a real focus. It has a virtual focus. Real image A real image is formed due to actual intersection of refracted or reflected rays. A real image can be obtained on a screen. A real image is inverted with respect to the object Virtual image A virtual image is formed when the refracted or reflected rays do not meet but appeared to be diverging from a point if they are produced backwards. A virtual image cannot be obtained on a screen. A virtual image is erect with respect to the object Power of lens: The power of a lens is a measure of deviation of light from its original path while passing through the lens. Numerically power is the reciprocal of the focal length of the lens. i.e., P = 1 f (metres) Unit: dioptre (D) Definition: z The power of a lens is said to be 1 dioptre if its focal length is 1 metre. Note: A lens of short focal length has more power. Power of concave lens is negative and power of convex lens is positive. For lenses in contact, power (P) = Volume 1 of 2 1 1 + + ...... f1 f2 Universal Tutorials X ICSE Physics 95 96 Limitations of the Eye: The e minimum distance d at which w an ob bject can be seen clearly by the na aked eye of a normal pers son is 25 cm. This is calle ed least dista ance of distin nct vision (i.e e. minimum a angle is 1 ). As the t object is brought clos ser than 25 cm vision is blurred b and clarity c is lost. Hen nce optical instruments lik ke magnifying glass, microscope etc are used. Simple Mic croscop pe (Mag gnifying g Glass s): AB is an object placed in fr ront of a con nvex lens be etween its op ptical cent tre O and fo ocus F1. A lig ght ray BP fr rom the poin nt B of the ob bject, incid dent parallel to the princ cipal axis, after a refractio on from the lens, pass ses through its focus F2 as a PF2. The e other ray BO O passing th hrough the op ptical centre gets refracte ed as OC without deviation. The tw wo refracted d rays PF2 and OC appe ear to mee et at a point B B when prod duced backw wards. Thus A B A is the virtual, mag gnified and erect e image of o the object AB. A Magnification: z It is define ed as the ratio of the size e of the image to the size e of the objec ct. M= height of image e v I = = height of objec ct O u z Magnifying power (m) ) of a simple microscope is 1+ D . Wh here D is lea ast distance of o distinct f vision and d f is focal len ngth. z Magnifying power is greater g for a lens l of shorte er focal length and vice versa. Dete erminatio on of foc cal leng gth of co onvex len ns: z Distant ob bject method d Principle: A parall lel beam incident from a distant obje ect converges s in the foca al plane of the len ns. z By Auxilia ary plane mir rror method, f = 96 x+y 2 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 05: Refraction through a Lens 97 z Explanation: When the object lies in the focal plane of the lens the rays starting from O after refraction travel parallel to the principle Axis and strike the mirror at 90 . As i = 0, r = 0.the rays are reflected back by the plane mirror along the same path. They strike the lens as a parallel beam. The lens converges them on its focal plane and hence image is formed just above O. Uses of lenses: Convex lens Objectives of telescopes, slide projector, camera Spectacles for persons suffering from hypermetropia (long sight) Magnifying glass Concave lens Eye lens of Galilean telescope Spectacles for persons suffering from Myopia (short sight) Typical Solved problems: An object 4 cm high is placed 20 cm in front of a convex tens of focal length 10 cm. Calculate the size and the position of the image. Sol: 2 A 1 1 X X O 5 4 3 u F 2 1 C 1 1 2 F1 2 3 v Y 4 5 I B Scale 1 cm = 4 cm Object height =0 = 4 cm Object distance = u = 20 cm Focal length of lens =f = 10 cm Image height =I =? Image distance = v = ? i) Draw a horizontal line to represent the principal axis of the lens ii) Draw the centre line of the lens AB perpendicular to the axis with its optical centre C on the principal axis iii) Mark two foci (F and F1) of the lens (2.5 cm each) on either side of AB. iv) At a distance of 5 cm from C place the object OX v) Two rays are required to be constructed: a) A ray XX parallel to the principal axis which after cutting through the centre passes through focus F1. b) A ray XC passing through the optical centre and extended to intersect the earlier ray at I. I is the image of point X. Thus, the image IY is located. Rays pass through the image, so it is real. IB = 5 cm, Distance from optical centre = 5 4 = 20 cm Nature of Image: Real, inverted, same size as the object. actual height of image = 1.0 4 = 4.0 cm IY = 1.0 cm, Ans: Image size is 4 cm; image distance is 20 cm Volume 1 of 2 Universal Tutorials X ICSE Physics 97 98 REVIEW QUESTIONS: Direct questions: q 1) What is a lens? ? 2) State two differences betw ween a conve ex and a conc cave lens. 3) Sh how by a dia agram the re efraction of two light ray ys incident parallel p to th he principal axis a on a co onvex lens by y treating it as a a combina ation of a glas ss block and d two triangul lar glass pris sms. 4) Ho ow does the action of a convex lens s differ from that of a concave lens o on a parallel l beam of light incident on o them? Dra aw diagrams to illustrate your y answer r. 5) De efine the term m principal ax xis of a lens. . 6) Ex xplain optical l centre of a lens with the e help of a pr roper diagram m/diagrams. 7) De efine the term m principal foci f of a conv vex lens and d illustrate yo our answer w with the aid of proper dia agrams. 8) De efine the term m focal length of a lens. 8) A ray of light, after a refractio on through a concave len ns emerges parallel to the principal axis. a Draw a ray r diagram to show the incident ray and its corre esponding em mergent ray. 9) A ray of light after a refractio on through a convex lens emerges pa arallel to the principal axis s. Draw a ray y diagram to o show it. 10) A parallel obliq que beam of light falls on o a i) conve ex lens, (ii) concave c lens s. Draw a diagram in ea ach case to show s the refr raction of ligh ht through the e lens. 11) W What are the three princi ipal rays tha at are drawn n to construc ct the ray di iagram for th he image for rmed by a lens? Draw dia agrams to su upport your answer. a 12) Distinguish bet tween a real and a virtua al image. 13) An n object is placed p in fro ont of a con nverging len ns at a dista ance gre eater than tw wice the foca al length of the lens. Dra aw a ray diag gram to show the for rmation of im mage. State it ts three char racteristics. 14) A convex lens forms an im mage of an object equal to t the size of f the ob bject. Where is the obje ect placed in n front of the lens? Dra aw a dia agram to illus strate it. 15) A linear object t is placed on the axis of f a lens. An image is formed by refra action in the lens. For all positions of f the object on o the axis of o the lens, th he positions of the image e are always s between the e lens and th he object. Na ame the lens and draw a ray diagram to show it. 16) In each of the following ca ases, where must m an obje ect be placed d in front of a convex len ns so that the e image form med is b) of same size a) at infinity, e as the obje ect, c) inverted and d enlarged? 17) Dr raw a diagram m to show ho ow a converg ging lens can n form a real l and enlarge ed image of an a object. 18) Dr raw a ray dia agram to sho ow how a co onverging len ns is used as s a magnifyin ng glass to observe o a sm mall object. Mark M on your r diagram the e foci of the lens and the e position of the eye, and d indicate the e position at which the im mage will be seen. 19) State the chan nges in the position, p size e and nature of the image of an object when brou ught from inf finity up to a convex lens. Illustrate yo our answer by b drawing di iagrams. 20) A convex lens has focal le ength equal to t 25 cm. An n object is placed p at a d distance 12.5 5 cm from the e lens. Draw w a diagram to o find the po osition of the image. 21) An n illuminated slit is kept at a a distance e 40 cm in fro ont of a conv vex lens of fo ocal length 15 1 cm. By dra awing, find th he position of o the screen to obtain the e image. 22) Th he diagram below b in Fig. shows two in ncident rays P and Q which emerge a as parallel ra ays R and S respectively. . The approp priate device used in the box A is: a) a convex len ns b) a concave le ens c) prism d) a concave mirror m 98 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 05: 0 Refraction n through a Lens L 99 23) Dr raw a neat la abeled ray diagram to loc cate the ima age formed by b a magnify ying glass. St tate three ch haracteristics s of the image e. 24) State two applications each h of a convex x lens and a concave len ns. APPLICATION TYPE: T Class Work: W 1) A ray of light incident at a point on the principa al axis of a convex lens s, passes un ndeviated thr rough the len ns. What spe ecial name is s given to this point on th he principal a axis? Draw a labelled dia agram to sup pport your an nswer. 2) State the cond dition for each h of the follow wing: a) a lens has both b) a ray passes b its focal lengths equal s undeviated through the lens. 3) Th he diagram below b shows s a lens as a combinatio on of a glass block and tw wo prisms. (i) ) Name the lens l formed by the comb bination. (ii) What is the line XX called ?(iii) Complete the path of the incide ent ray AB after a passing thr rough the len ns. (iv) The final f emerge ent ray either r meets XX at a a point or ap ppears to co ome from a point on XX X . Label it as a F. What is this point ca alled? 4) In fig F1 and F2 are the two o foci of a th hin convex le ens and A is the incide ent ray. Com mplete the di iagram to sh how the pa ath of the ray y A after refra action throug gh the lens. 5) Study the diagram below N the len ns LL i) Name ii) What are the e points O, O O called? iii) complete th he diagram to o form the im mage of the object o AB. iv) ) State three characteristics of the ima age. 6) Co omplete the diagram d sho own in fig bel low to show the formatio on of image A B of the obje ect AB, of sa ame size. Name the len ns L and draw its i outline. What W are the e points O and O called d? LL Where is the object o located d? Where is the image formed? f Wha at are e the two oth her character ristics of the image? 7) Th he diagram given g below in Fig. show ws the positio on of an obje ect OA in rel lation to a co onverging len ns whose foc ci are at F1 and F2. i) Draw D two ray ys to locate the t position of o the image. ii) Measure an nd record the e distance of o the image from the op ptical centre of o the lens. iii) Describe the characteris stics of the im mage. iv) ) Describe ho ow the dista ance of the im mage from the lens and the size of the image change as the e object is moved m toward ds F1. 8) Fig g. shows an n object O and a its image e I formed by b a lens. Name N the len ns and show w it in the dia agram. Draw w suitable rays to locate the lens an nd its focus. State three characteristics of the im mage. 9) A candle of 2 cm c height is placed at a distance 15 cm in front of o a convex lens of focal length 10 cm m. Draw a sketch to find the t position and a size of th he image. 10) Th he diagram shows s the ex xperimental set s up for the e determination of foc cal length of a lens using g a plane mirror. i) Draw two rays r from th he point O of o the object pin to show w the formation of o image I at O itself. ii) What is the e size of the image I? Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 99 100 iii) State two more m characteristics of the e image I. iv) ) Name the distance d of th he object O from f the optic cal centre of f the lens. 11) Where must an n object be placed p in fron nt of a conve ex lens so tha at the image formed may y be a) at infinity b) of same size e as the obje ect c inverted an c) nd enlarged? ? W Home Work: 1) State the cond dition when a lens is calle ed equi-conve ex or equi-co oncave 2) Th he diagram below b shows s a lens as a combinatio on of a glass s block an nd two prisms s. i) Name the le ens formed by b the combi ination. ii) What is the e line OX called ? iii) Complete the t ray diagr ram and sho ow the path of the incide ent ray AB after pa assing throug gh the lens. iv) ) The final em mergent ray will either meet m OX at a point or app pear to come e from a poin nt on OX. Label the point as F. What is this po oint called? 3) In Fig F1 and F2 are the po ositions of th he two foci of o a thin conc cave len ns. Draw acc curately the path taken by b the ray A after it eme erges fro om the lens 4) In the t diagrams s below, XX represents the principa al axis, O the optical cent tre and F the e focus of th he lens. Com mplete the path h of rays A and a B as they y emerge out of the lens. 5) Co omplete the diagram d give en below to form f the imag ge AB. Name the e lens LL and a state the e three char racteristics of o the image e. Na ame a device e in which th his action of lens is used d. What is the po oints O and O O called? 6) wing diagram m in fig shows s an object A AB and a co onverging The follow lens L with foci F1 and a F2. Draw w two rays from the ob bject and complete the diagram to locate the e position of t the image. Mark M the image CD D. Clearly ma ark on the dia agram the po osition of the eye from where the e image can be viewed. State three characteristics of the image in relation r to the e object. 7) Th he following diagram d in Fig. F shows an n object O an nd its virtual image I for rmed by a le ens. Name the t lens and d show it in the diagram m. In the dia agram, draw w suitable ray ys to locate th he lens and mark the position of its focus. Meas sure the foca al length of th he lens and write w its valu ue in the dia agram. 8) Dr raw a diagra am to show how a conv verging lens is able to fo orm an imag ge of the sun. Hence su uggest a reas son for the te erm burning glass for a converging c le ens used in t this manner. 9) Th he diagram in Fig show ws a point so ource of ligh ht S on the axis of a co onverging len ns L and a pl lane mirror M, M at right an ngles to the axis. a Rays of light from the t source S return to their point of o origin. Dr raw a ray dia agram to illustrate this. Mark the focal length h of the lens on this dia agram. To what w point wi ill the rays return if the mirror m is mo oved away fro om the lens by b a distance e equal to the e focal length h? 100 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 05: Refraction through a Lens 101 10) How do the following change when a part of the lens is covered: (i) focal length (ii) intensity of light. MISCELLANEOUS: 1) What are the different kinds of lenses? Draw diagrams to illustrate them. 2) A concavo convex lens is: a) thick at the centre and thin at the periphery. b) thin at the centre and thick at the periphery c) thick at the centre with one surface plane d) thin at the centre with one surface plane. 3) Out of the two lenses, one concave and the other convex, state which one will show the divergent action on a light beam. 4) Show by a diagram, the refraction of two light rays incident parallel to the principal axis on a concave lens by treating it as a combination of a glass block and two triangular glass prisms. 5) Draw neat diagrams to show the convergent action of a convex lens and divergent action of a concave lens. 6) Define the term principal foci of a concave lens and show them with the help or proper diagrams. 7) Draw a diagram to represent the second focus of a concave lens. 8) Draw a diagram to represent the first focus of a convex lens. 9) Explain the following terms as applied to lenses and show them with the help of proper diagrams 10) Complete the following sentences: a) Both the focal lengths of a lens are equal when ___________ b) A ray of light passes undeviated after refraction from a thin lens when __________ c) If half part of a convex lens is covered, the focal length __________ change, but the intensity of image __________ d) A convex lens is placed in water. Its focal length _____________ e) The focal length of a thin convex lens is _________ than that of a thick convex lens 11) A ray of light directed towards the optical centre of a lens, after refraction: a) passes through the focus b) becomes parallel to the principal axis after refraction c) passes undeviated d) is reflected back 12) What do you mean by focal plane of a lens? 13) A lens forms an erect, magnified and virtual image of an object placed between its optical centre and principal focus. Name the type of lens and draw a ray diagram to show the formation of such an image with the lens mentioned by you. 14) Classify as real or virtual, the image of a candle flame formed on a screen by a convex lens. Draw a ray diagram to illustrate how the image is formed. 15) Show by a diagram that a diverging lens cannot form a real image of an object placed anywhere on its principal axis. 16) A lens forms an inverted image of an object. What kind of lens is this? 17) A lens forms an upright and magnified image of an object. Name the lens. State whether the image is real or virtual? 18) Name the lens which always forms an erect and virtual image. State whether the image is magnified or diminished? 19) A lens forms an upright and diminished image of an object irrespective of its position. What kind of lens is this? 20) Give two characteristics of the image formed by a concave lens. 21) Give two characteristics of the virtual image formed by a convex lens. 22) What will be the nature of the image real or virtual image formed by a convex lens? Volume 1 of 2 Universal Tutorials X ICSE Physics 101 102 23) A concave lens forms the image of an object which is a) virtual, inverted and diminished b) virtual, upright and diminished c) virtual, inverted and enlarged d) virtual, upright and enlarged. 24) Where should an object be placed in front of i convex lens so as to form an upright and enlarged image? Will the image be real or virtual? 25) Complete the following table 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 102 Type of lens Position of object Nature of image Size of image Convex Between optic centre and focus Convex At focus Concave At infinity Concave At any distance Complete the following sentences a) An object is placed at a distance of more than 40 cm from a convex lens of length 20 cm. The image formed is real inverted and b) An object is placed at a distance 2f from convex lens of focal length f. The size of image formed is that of object c) An object is placed at a distance 5 cm from a convex lens of focal length 10 cm. The image formed is virtual, upright and State whether the following statements are true or false by writing TIF against them. a) A convex lens has a divergent action and a concave lens has a convergent action. b) A concave lens if kept at a proper distance from an object can form its real image. c) A ray of light incident parallel to the principal axis of a lens, passes undeviated after refraction. d) A ray of light incident at the optical centre of lens, passes undeviated after refraction. e) A concave lens forms a magnified or diminished image depending on the distance of object from it. Where will the image be formed if an object is kept in front of a concave lens at a distance equal to its focal length? Draw a diagram to illustrate your answer. State the changes in the position, size and nature of the image of an object when brought from infinity up to a concave lens. Illustrate your answer by drawing diagrams. A convex lens produces an image on a screen twice the size of the object. The distance between the object and screen is 45 cm. Find the distance of lens from the object and its focal length by drawing a ray diagram. An object of size 5 cm is placed at a distance 15 cm from a concave lens of focal length 10 cm. Draw a ray diagram to find the size and position of the image formed. Define the power of a lens. In what unit is it expressed? How is the power of a lens related to its focal length? How does the power of a lens change if its focal length is doubled? What is the sign (+ or ) of power of a lens related to its divergent or convergent action? What is a magnifying glass. State its two uses. Define magnifying power of a simple microscope. How can it be increased? Describe in brief how would you determine the approximate focal length of a convex lens. Describe how you would determine the focal length of a converging lens. Using a plane mirror and one pin. Draw a ray diagram to illustrate your answer. Name two practical application of a concave lens. Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 05: 0 Refraction n through a Lens L 103 PREVIOUS S BOARD QU UESTIONS: 1) Yo ou are provided with a printed piec ce of paper. Using this paper, how will you dif fferentiate [2012] be etween a con nvex lens and d a concave lens? 2) A converging lens is used d to obtain an a image of f an object placed p in fro ont of it. The e inverted im [2012] mage is forme ed between F2 and 2F2 of f the lens. i) Where W is the e object place ed? ii) Draw a ray diagram d to ill lustrate the formation f of the t image ob btained. 3) i) When does s a ray of ligh ht falling on a lens pass th hrough it und deviated? ii) Which lens can produce [2011] e a real and inverted ima age of an obje ect? 4) (2009) T Type of lens s Position ns of object t Nature of o image Size of ima age C Convex At F C Concave At infinity y 5) i) Copy and co omplete the diagram to show the for rmation of the e image of th he object AB. ii) what is the name n given to t X? L A B P 6) i) The T diagram m below show ws a ray of white w light PQ Q coming fro om an n object PQ Q coming fro om an objec ct P and in ncident on the t su urface of a thick glass plane mirro or. Copy the e diagram and a co omplete it to show the for rmation of th hree images of the object tP as s formed by the mirror. A O X X L Q B C D ii) Which image e will be the brightest ima age? 7) Dr raw a ray dia agram to illustrate the de etermination of the focal length of a convex lens using an (2008) au uxiliary plane e mirror 8) A linear object t is placed on the axis of f a lens. An image is formed by refra action in the lens. For all positions of f the object on o the axis of o the lens, th he positions of the image e are always s between the (2008) e lens and th he object. i) Name the le ens ii) Draw a ray diagram to show s the formation of the e image of an object plac ced in front of o the lens at any posit tion of your choice c excep pt infinity. 9) An n object is placed in front t of a conver rging lens at a distance greater g than twice the foc cal length (2007) of the lens. Dra aw a ray diag gram to show w the formati ion of the image 10) Th he given ray diagram illus strates the ex xperimental set s up for the e determinat tion of the foc cal length of a converging g lens using a plane mirr ror. i) State the magnification m of the image e formed. ii) Write two characteristic c cs of the imag ge formed. iii) What is th he name giv ven to the distance d bet tween the object and d optical ce entre of the e lens in th he above diagram? 11) Which physica al quantities do d the follow wing units rep present? a) Dioptre Volume 1 of 2 b) Kelvin Universal Tu utorials X IC CSE Physics s 103 104 12) A ray of light, after refrac ction through h a concave lens, emerg ges parallel to the princ cipal axis. Dr raw a ray dia agram to show the inciden nt ray and its s correspond ding emergen nt ray. 13) State three cha aracteristics of the image e of an exten nded source, formed by a concave len ns. 14) An n erect, diminished and virtual v image e is formed when w an obj ject is placed d between th he optical ce entre and prin ncipal focus of o a lens. i) Name the ty ype of lens, which w forms the above im mage. ii) Draw a ray diagram to show s the form mation of the e image with the above c characteristic cs. 15) Given OC is equal to the focal f length of o the lens; copy c the diag gram in O1 J yo our answer book. b Draw two rays fro om the linea ar object OO O1, and C ob btain the imag ge formed by y the lens. O J is image 16) Dr raw a ray dia agram to illus strate the act tion of a conv vergent lens as a reading g lens or a magnifying m gla ass. 17) Is it possible to o burn a pie ece of paper using a convex lens in daylight d with hout using matches or an ny direct flam me? Draw a diagram d to su upport your answer. a 18) An n object is pl laced in fron nt of a conve ex lens such that the ima age formed h has the sam me size as tha at of the obje ect. Draw a ray r diagram to t illustrate th his. 19) Th he diagram given alongside shown an object O and its im mage I. Co opy the diag gram and dra aw suitable rays to loca ate the lens and its foc cus. Name th he type of len ns in this cas se. 20) Th he diagram shows s a poin nt source of light l S, a con nvex lens L and a a plane p mirror M. These are placed su uch that rays of light, from mS ret turn to it afte er reflection from M. i) What is the e distance OS S called? ii) To which po oint (left of S, S on S, or rig ght of S) will the rays retu urn, if M is move ed to the left and brought t in contact with w L? ANSWERS: Previous s Board Que estions: 1) On n seeing the e printed pie ece of paper by a conv vex lens, kee eping it very y close to th he paper, en nlarged and erect e letters are a seen; wh hile with the concave c lens s at the same e position, diminished an nd erect letters are seen. 2) i) The T object is s placed beyo ond 2F1. ii) The ray diag gram is given n, 4) Type of lens T s Position ns of object t Nature of image Size of f image C Convex At F Real and d inverted Very much magnified C Concave At infinity y Virtual an nd upright Highly diminished 12) i) same s size ii) a) Real & inv verted. b) Fo ormed at infin nity on the ot ther side of the lens. Foc cal length of the t lens. 13) a) Power of len ns b) Temperature e. 14) i) See S figure. 104 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 05: 0 Refraction n through a Lens L 105 16) i) Concave C lens. ii) See figure given g alongside. 17) Se ee figure alon ngside. 1 1 18) When an obje ect is placed d within the focal length of the len ns, a virtual up right an nd magnified d image is formed f (se ee figure alongside). 19) ii) Yes, It can be done by focusing sun n rays on pa aper with the help of a co onvex lens. When W the ray ys of sun pass through th he convex le ens and pape er is placed at a its focus o of the sun are e focused at F. 22) a) As shown in n diagram, ra ays of light fr rom S return n to it after re eflection from m the mirror M. M This is po ossible only when w S is lo ocated at the e principal fo ocus of the e lens. Hen nce, the distance OS is s called the e focal len ngth of the le ens. b) Rays will al lways return to S, whate ever be the position p of the mirror, , held paral llel to the lens, becau use the em mergent rays s form a para allel beam of o light which h, when ref flected back from the mirror M, will meet m at the focus f S aft ter passing through the le ens L. Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 105 106 Chapter 06: Spectrum Chapter Map: Deviation of Light Factors Dispersion Recombination of white light Electromagnetic Spectrum Common Properties Colours in white light Scattering of light Deviation: When a ray of light passes from one medium to another medium, it gets deviated from its path. For deviation to take place, the angle of incidence should not be zero. Deviation takes place at the boundary of the two media. The magnitude of deviation depends on the angle of incidence of the light ray and the refractive index of the second medium with respect to the first medium. Let 1 be the angle of deviation at the first surface AB, then 1 depends on the angle of incidence and the refractive index of glass with respect to air. Let 2 be the angle of deviation at face AC. 2 depends on the angle of the prism A (because angle of incidence on this surface depends on the angle of the prism) and the refractive index of air w.r.t. glass. Total deviation = 1 + 2 Factors on Which Angle of Deviation ( )Depends: Angle of Incidence (i): As angle of incidence increases, decreases, reaches a minimum value and then increases. Angle of prism (A): increases with increase in the angle of the prism. Refractive index of the material of the prism ( ): For a given angle of incidence i, the prism with high value of produces greater deviation. Colour or wavelength of light: decreases with increase in wavelength of light. If the incident light has many colours then the emergent beam has colours arranged in a definite order. It is because different colours travel with different speed in glass and deviate through different angles. The speed of light decreases with decrease in wavelength. Hence violet has least speed in glass while Red has the maximum speed. (R. . of violet is more than Red). 106 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 06: 0 Spectrum m 107 Disp persion n of Light: Ligh ht having sing gle waveleng gth (colour) is called mon nochromatic light. Ligh ht of many wa avelengths (colours) is called polychr romatic light. . White light is a mixture m of 7 colours. c Whe en white ligh ht falls on prism, p it split ts into its co omponent co olours. This phenomena is called Dispersion of lig ght . Disp persion occu urs because e different co olours travel with differe ent speeds in glass.and d deviate thro ough different t angles. The e seven colours obtained d by the disp persion are VIOLET, V IND DIGO, BLUE E, GREEN, YELLOW, Y ORE ENGE, AND RE. (VIBGY YOR) in the increasing i order of wave e lengths. Th he red colour r deviates the least while violet v deviates the most. The e band of colo ours obtained d after dispe ersion is calle ed spectrum. New wton discovered that whit te light consist of large nu umber of wav velengths. A pr rism itself pro oduces no sp pectrum (colours). The T wavelength is the characteristic of o the colour irrespective if its origin. Colour Frequ uency Range in 1014Hz Viole et 6.37 7.5 7 Indig go 6.47 6. .73 Blue e 6.01 6. .47 Gree en 5.19 6. .01 Yello ow 5.07 5. .19 Oran nge 4.84 5. .07 Red 3.75 4. .84 10 Note: : 1 8 = 10 m. Waveleng gth Range A 4000 0 to 4460 4460 0 to 4640 4640 0 5000 5000 0 5780 5780 0 5920 5920 0 6200 6200 0 8000 Reco ombinat tion of White W Lig ght: T The 7 colou urs of light can be rec combined to p produce whit te light. This T was dem monstrated by b Newton s colour c Disc. When W this dis sc is rotated rapidly all co olours blend t together and a sensa ation of wh hite light is p produced on the retina of f the eye. The T Recomb bination can also a be demo onstrated using two prism ms. Prism m itself pr roduces no n colour r: V W When white light l is made e to fall on a prism, p it undergoes dispe ersion. When W a slit is placed in front f of gree en colour as shown abov ve and the lig ght is made to fall on a another prism m, only green n light is seen. This prove es that the pr rism produce es no colour. . Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 107 108 Electromagnetic Spectrum: The group of frequencies or wave lengths emitted by the sum is called electromagnetic spectrum. The portion of the spectrum between the Red end and violet end is called visible spectrum The part of the spectrum just before the violet end is called ultraviolet spectrum The part of the spectrum just beyond the red end is called ultraviolet spectrum Properties and uses of Different Radiations of electromagnetic spectrum: Gamma rays: Wavelength: less than 0.01A Source: obtained from nuclear radiations Property: They can penetrate through human body and cause biological damage. Use: In industry to check welding In medicine to kill cancer cells X-rays: Wavelength: 0.1 A to 100 A Source: by high energy particles striking heavy metal plates Property: Penetrate human flesh but not bones Use: detection of fractions, CAT scan, to study atomic arrangement of crystals, detection of concealed precious Ultraviolet rays: Wavelength: 100 - 4000 Source : Electric arc electric spark Property: z They are absorbed by glass prism but not by quartz. z Ultraviolet radiations can pass through quartz, but they are absorbed by glass. The ultraviolet spectrum is therefore obtained by passing the radiations through a quartz prism instead of a glass prism. For the same reason the ultraviolet bulbs have the envelope made of quartz instead of glass. z These radiations travel in a straight line with a speed of 3 108 m s 1 in air (or vacuum). z They are usually scattered by the dust particles present in the atmosphere. z They obey the laws of reflection and refraction. z They strongly affect the photographic plate as they are chemically more active. z They produce fluorescence on striking a zinc-sulphide screen. z They cause health hazards like skin cancer if our body is exposed to them a long period. Uses: z For sterilizing purposes. z For detecting the purity of gems, eggs, ghee, etc. z In producing vitamin D in food of plants and animals. Detection: z When UV rays pass through silver chloride, it turns violet and finally dark broom. 108 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 06: Spectrum 109 z They are chemically more active than visible light. Hence are called actinic rays. Visible light: Wave length: 4000 - 8000 Source: Sun, electric bulb, hot objects Property: objects can be seen due to visible light Use: Photosynthesis, photography Infrared Radiations: Wavelength: 8000 to 107 Source: all heated objects Properties: z They travel in straight lines as light does, with a speed equal to 3 108 m s 1 in vacuum (or air). z They obey the laws of reflection and refraction. If a source of heat (say, an infrared lamp) is placed at the focus of a parabolic mirror, a parallel infrared beam is obtained. A burning glass (i.e., a convex lens) focuses the infrared radiations of short wavelengths from the sun on a paper due to which the paper chars (or burns). z They do not affect the ordinary photographic film. However, they affect a specially treated photographic film. z They are absorbed by glass, but they are not absorbed by rock salt. z They are detected by their heating property using a thermopile or a blackened bulb thermometer. Uses: z The infrared radiations are used for therapeutic purpose by doctors. z They are used in photography at night and also in mist and fog because they are not much scattered, so they can penetrate appreciable through it. z Infrared lamps are used in dark rooms for developing photographs since they do not affect the photographic film chemically, but they provide some visibility. z They are used as signals during was as they are not visible and they are not absorbed much in the medium. z They are used in remote control of television and other gadgets. Microwaves: Wavelength: 107 - 1011 Source: electronic device like klystron tube Property: Travel straight without much deviation Use: Satellite communication, microwave ovens, radar communication Radio waves: Wavelength: above 1011 Source: Oscillatory circuits Property: Properties of electromagnetic radiations Use: Radar, Radio and TV communication Volume 1 of 2 Universal Tutorials X ICSE Physics 109 Sources Ritter Newton Hershell Hertz Marconi 1016 7.5 1014 7.5 1014 3.7 1014 3.7 1014 1011 1011 107 Below 107 Visible light Infrared waves (Invisible) Microwaves (Invisible) Radiowaves (Invisible) Electrical circuits Electrical circuits Sunlight, light from electric bulb, flame, white hot bodies. Lamp with thoriated filament heated silicon carbide rod, red hot bodies Becquerel and Curie Ultraviolet (Invisible) Nuclear changes in the radioactive nuclides such as U, Th etc, cosmic rays When highly energetic electrons are stopped by a heavy metal target of high melting point Sunlight, arc lamp or spark Discoverer Roentgen Hz 21 10 1019 Frequency in 1019 1016 Name of the wave Gamma rays (Invisible) X rays (Invisible) Oscillatory electrical circuit. Heat effect is more. The mercury rises rapidly when a thermometer with blackened bulb is kept in these radiations. Oscillatory electrical circuit. Other objects can be seen in its presence. The photographic plate wrapped in a black paper or kept in a wooden box is affected By their chemical activity. Photographic plates get affected. It causes fluorescence. By their large penetrating power Method of detection Obey laws of reflection, refraction. Do not affect ordinary photography film. They are absorbed by glass but not by rock salt. They are less scattered Travel in straight line. Do not bend much Longest wavelength Can pass through quartz but are absorbed by glass. (UV spectrum is hence obtained by quartz prism). They obey laws of reflection and refraction Consists of 7 colours. Travel in straight line in a medium Most energetic electromagnetic radiations, can penetrate through human body Can penetrate human flesh but not bones Properties Satellite communication, radar communication, micro ovens. Radar and Television communication. Photography at night and in fog as they are not scattered much. In T.V. remote controls. As signals in war since they are not much absorbed by the medium Cause sensation of sight Sterlising purposes, checking purity of gems eggs etc, producing vitamin D in food of plants and animals Detect fractures, study atomic arrangement in crystals Kill cancer cells and to check welding Uses The electromagnetic spectrum consists of invisible and visible region. Portion of spectrum beyond red end is Infra Red and before violet end is ultra violet. Both the regions on either side of visible spectrum are invisible. Electromagnetic Spectrum: Chapter 06: Spectrum 111 Common properties of electromagnetic waves They travel with same speed in air (3 108 m/s). They are not affected by electric and magnetic fields. They are transverse waves. They show reflection and refraction. Distinction between the ultraviolet, visible and infrared radiations: Ultraviolet radiations Visible radiations Infrared radiations They have the wavelength in They have wavelength in the They have wavelength in the the range of 100 8 to 40008. range of 4000 8 to 8000 8. range of 80008 to 107 8 They are invisible. They are visible They are invisible They produce no heating They produce slight heating They produce more heating effect. effect. effect. They affect the photographic They affect the photographic They do not affect the plate. plate. photographic plate. They cause fluorescence on They do not cause They do not cause zinc sulphide screen. fluorescence fluorescence They cause health hazards They do not affect the body. They do not affect the body. like skin cancer on the body. Scattering of Light: When white light from sun enters the earth s atmosphere, the light gets scattered (i.e. the light spreads in all directions) by the dust particles, free water molecules and the molecules of the gases present in the atmosphere. The scattering of light by the air molecules was first studied by the scientist Rayleigh. The scattering is the process of absorption and then re emission of light energy. The intensity of scattered light is found to be inversely proportional to the fourth power of wavelength of light (i.e. I 1/ 4) But if the size of air molecules is bigger than the wavelength of incident light, the intensity of scattered light is the same for all wavelengths of white light. Effects of Scattering: Blue colour of sky: As the light travels through the atmosphere, it gets scattered in different directions by the air molecules present in its path. The blue (or violet) light due to its short wavelength is scattered more as compared to the red light of long wavelength. The blue scattered light reaches our eye due to which the sky opposite the sun is seen blue. White colour of sky at noon: At noon, the sun is above our head, so we get light rays directly from the sun without scattering Hence the sky is seen white. Red colour of sun during sunrise and sunset: z During the sun rise and sunset, the light from sun has to travel the longest distance of atmosphere. z The light travelling from sun looses blue light of short wavelength due to scattering. z As a result, the sun and region near the sun is seen red since white blue = red (nearly) Volume 1 of 2 Universal Tutorials X ICSE Physics 111 112 Black colour of sky in absence of atmosphere: z In the absence of atmosphere, there will not be any scattering of light and so no light will reach our eye i.e. the sky will appear black. z On the moon, since there is no atmosphere, there is no scattering of light from sun reaching the moon s surface. Hence the sky will appear black to an observer on the moon s surface. z When an astronaut goes above the atmosphere of the earth in a rocket, he sees the sky black, but to him the earth appears blue due to the blue colour of sunlight scattered by the earth s atmosphere. White colour of clouds z The clouds are nearer the earth s surface and they contain dust particles and aggregates of water molecules of a size bigger than the wavelength of visible light. z Therefore the dust particles and water molecules present in clouds scatter all colours of incident white light from sun to the same extent and hence when the scattered light reaches our eye, the clouds are seen white. Use of red light for the danger signal z Since the wavelength of red light is the longest in the visible light, the light of red colour is scattered least by the air molecules of the atmosphere and therefore it can reach to a longer distance. Scattered blue light Observer Sun Scattered blue light Earth Earth s atmosphere REVIEW QUESTIONS: Direct questions: 1) How does the deviation produced by a triangular prism depend on the colours (or wavelengths) of light incident on it? Which colour is deviated the most and which the least? 2) Define the term dispersion of light. 3) Explain the cause of dispersion of white light through a prism. 4) Explain briefly, with the aid of a neat labeled diagram, how white light gets dispersed by a prism. 5) How does the speed of light in glass change on increasing the wavelength of light? 6) What do you understand by the term spectrum? 7) What is a spectrum? Draw a labelled ray diagram to show the formation of spectrum of white light by a prism. 8) i) Draw a diagram to show the splitting of white light by a prism into its constituent colours. ii) Draw another diagram to show how e colours of spectrum of white light can be combined to give the effect of white light. 9) What is the range of wavelength of different colours in the spectrum of white light? 10) Name the seven prominent colours of white light spectrum in order of their increasing frequencies. 11) Name four colours of the spectrum of white light which have wavelength longer than blue light. 12) What is the range of the wavelength of the following electromagnetic waves? a) Gamma rays, b) X rays, c) Ultraviolet d) Visible e) Infrared f) Micro waves and g) Radio waves 13) Name the region beyond (i) the red end and (ii) the violet end, of the spectrum. 112 Universal Tutorials X ICSE Physics Volume 1 of 2 Chapter 06: 0 Spectrum m 113 14) What do you understand by the invisi ible spectrum m? How will you investig gate the existence of rad diation beyond the red an nd violet end ds of the spectrum? 15) State the appr roximate ran nge of wavel length assoc ciated with th he ultraviolet rays and th he visible light. 16) Write the range e of wavelen ngth of (i) the e ultraviolet spectrum, s and (ii) the infra ared spectru um. 17) Na ame two elec ctromagnetic c waves of fr requency gre eater than th hat of violet li ight. State one use of ea ach. 18) Na ame two sources, each of o infrared rad diations and ultraviolet ra adiations. 19) What are infrared radiation ns? How are they detecte ed? State two o properties and one use e of these rad diations. 20) Me ention three properties of f infrared rad diations similar to the visible light. 21) Give two such properties of o infrared rad diations whic ch are not tru ue for visible light. 22) Ho ow would the e sky appear r when seen from the spa ace (or moon n)? Give reas son for your answer. a 23) What is meant t by scatterin ng of light? 24) Ho ow is the in ntensity of scattered s light related with w the wav velength of incident ligh ht? State co onditions whe en this relatio onship holds. 25) When sunlight t enters the earth s atmo osphere, state which col lour of light is scattered the most an nd which the least. 26) Th he source of ultraviolet lig ght is: a) Electric bulb b b) Red hot iron n ball c) Sodium S vapo our lamp d) C Carbon arc-lamp. N NUMERICAL S: Class Work: W 1) An n electromag gnetic wave has h a frequency of 500 MHz M and a wavelength w of f 60 cm. Calc culate the ve elocity of the wave. Name e the medium m through wh hich it is trave elling. [3 108 m s 1, air] 2) Ca alculate the frequency f of yellow light of wavelengt th 5500 8. The T speed of light is 3 108 ms 1 [5.4 1014 Hz] Home Work: W 1) Th he frequency y range of vis sible light is from f 3.75 1014 Hz. Calc culate its wa avelength ran nge. Take 8 1 sp peed of light = 3 10 ms s [4000 8 to o 8000 8] 2) Th he wavelengt th of X rays in 0.01 8. Calculate its fr requency. [3 1020 Hz] APPLICATION TYPE: T Class Work: W 1) Na ame the fact tors on whic ch the deviat tion produced by a prism m depends a and state how does it de epend on the em. 2) Fig g. shows a thin beam of white light from f a sourc ce S striking on on ne face of a prism. p a) Complete the t diagram m to show th he effect of prism on the t beam and to t show what is seen on the screen. b) A slit is pla aced in betw ween the pris sm and the screen s to pa ass only the ligh ht of green colour. c What will you then n observe on the screen? ? c) What conclusion do you u draw from the t observat tion in part (b b) above? 3) A ray of white light is passe ed through a glass prism m and spectru um is obtaine ed on a scree en. Name the e seven colo ours of the sp pectrum in or rder. Do the colours have e the same w width in the spectrum? Which of the colour of the spectrum s of white light de eviates (i) the most, (ii) th he least? Volume 1 of 2 Universal Tu utorials X IC CSE Physics s 113 114 4) Co omplete the ray diagram given below w to show the e nature of light produce ed on the sc creen. 5) Ar rrange the fo ollowing in the t order of their increa asing wavele ength X-rays s, infrared ra ays, radio wa aves, gamma a rays and micro m waves 6) Na ame the high energetic invisible ele ectromagnetic wave whic ch helps in study of str ructure of cry ystals. State one more us se of it. 7) Tw wo waves A and B have e wavelength h 0.01 8 and d 9000 8 respectively. N Name the tw wo waves. Co ompare the speeds s of the ese waves when w they travel in vacuum. 8) Na ame three pr roperties of ultraviolet u rad diations whic ch are similar r to visible lig ght. 9) Ex xplain the following: i) Infrared rad diations are used u for phot tography in fog. f ii) Infrared rad diations are used u for sign nals during war. w iii) The photog graphic darkr rooms are pr rovided with infrared i lamp ps. iv) ) A rock salt prism is used instead of a glass prism m to obtain th he infrared s spectrum. v) A quartz prism is required for obtain ning the spec ctrum of the ultraviolet u light. vi) ) Ultraviolet bulbs b have a quartz enve elope instead d of glass. 10) Th he colour of the t sky oppo osite the sun is blue Give reason. 11) Th he sky at noo on appears white. w Give re eason. 12) In the formatio on of spectrum m by a prism m i) Which colour is deviated least? ii) Which colour is deviated maximum? ? iii) After which colour from the red end does violet lie? iv) ) After which colour from violet does green g colour r lie 13) Th he following figure repres sents a part of electromagnetic spec ctrum extend ding on eithe er side of vis sible spectrum E F A B C Visible lig ght D i) ii) iii) iv) ) v) Name the radiations r A, B, C, D, E, F. F How are the e radiations represented by C and D detected? Give two pr roperties of C and D. Give two us ses of C, D. Name the visible v radiati ion X, and Y? ? Which of th hem has long ger waveleng gth? 14) Fin nd the error if any in the figure f and co orrect it if the ere is an erro or. Yello ow R V Lig ght 15) Na ame the wav ves used in i) Radar ii) to detect pu urity of ghee and gems. iii) right photog graphy. iv) ) fractures in bones and teeth. t v) Strongly aff fect photogra aphic plate and a turn silve er chloride pa aper brown. 114 Universal Tu utorials X IC CSE Physics s Volu ume 1 of 2 Chapter 06: Spectrum 115 Home Work: 1) The diagram below shows the path taken by a narrow beam of Yellow 60 yellow monochromatic light passing through an equiangular glass Yellow prism. Now the yellow light is replaced by a narrow beam of white light incident at the same angle. Draw another diagram to show the passage of the beam through the prism and label it to show the effect of prism on the white light. 2) i) If a monochromatic beam of light undergoes minimum deviation through an equi-angular prism, how does the beam pass through the prism, with respect to its base? ii) If white light is used in same way as in (i) above, what change is expected in the emergent beam? iii) What conclusion do you draw about the nature of white light in part (ii)? 3) The wavelengths for the light of red and blue colours are roughly 7 10 7 m and 4 10 7 m respectively. Which colour has the greater speed in vacuum? Which colour has greater speed in glass? 4) Give a list of at least five radiations, in the order of their increasing frequencies, which make up the complete electromagnetic spectrum. Which of these has the highest penetrating power? 5) A wave has a wavelength of 0018. Name wave. State its one property different from light. 6) Name the radiations of wavelength (i) longer than 8 10 7 m, (ii) shorter than 4 10 7 m. 7) What are ultraviolet radiations? How are they detected? State two properties and one use of ultraviolet radiations. 8) Give two properties of ultraviolet radiations which differ from the visible light. 9) The danger signal is red. Why? 10) During sunrise and sunset, the sun appears red why? 11) The clouds are seen white. Why? 12) A ray of white light is a mixture of red, blue and green White White is incident as shown. Complete your diagram to show Light Light the emergent light. 13) The wavelength of red is 8000 and violet is 4000 i) Will they have same speed in glass? ii) Will they have same speed in air? R 14) Find the errors in the figure Yellow V Light 15) A beam of white light is incident as shown: i) Copy the diagram and complete it till light emerges out from the prism (c= 42) ii) Can prism dispense light? Explain iii) State the angle of incidence on face PQ, PR, QR for all 7 colours. iv) What would be the colour of light which emerges out? P 60 White light 60 Q 60 R MISCELLANEOUS: 1) Dispersion of light by a glass prism takes place because: a) the light of different colours have different intensities. b) the light of different colours have different speeds in a medium. c) the light of different colours have different frequencies. d) the light of different colours have different energies. 2) Briefly describe an experiment to show that a prism itself produces no colour. 3) Which of the following is correct: b) yellow > green > blue a) blue > yellow > green Volume 1 of 2 Universal Tutorials X ICSE Physics 115 116 c) yellow > blue > green d) green > blue > yellow 4) Give one use each of (i) microwaves (ii) ultraviolet radiation (iii) infrared radiations and (iv) gamma rays. 5) The following is a list of waves Ultraviolet rays, light waves, X-rays, gamma rays, infrared rays. Fill in the blanks in the sentences (i) to (iv) with the name of the appropriate ray/wave. i) ___________ are the waves of highest frequency. ii) ___________ are used for taking photographs of objects in the dark. iii) __________ are produced by changes in the nucleus. iv) _________ are the electromagnetic waves of wavelength nearly 0.1 nm. 6) A radiation X is focused by a proper device on the bulb of a thermometer. Mercury in the I thermometer shows a rapid increase. The radiation X is a) infrared radiation b) visible light c) ultraviolet radiation d) X-rays. 7) In white light of sun, maximum scattering by the small dust particles present in the earth s atmosphere is for: a) red colour b) yellow colour c) green colour d) blue colour PREVIOUS BOARD QUESTIONS: 1) i) ii) 2) i) ii) 3) i) 4) 5) 6) 7) 8) 9) 10) What is meant by dispersion of light? In the atmosphere which colour of light gets scattered the least? [2012] How is the refractive index of a medium related to its real depth and apparent depth? Which characteristic property of light is responsible for the blue colour of the sky? [2011] Suggest one way, in each case, by which we can detect the presence of: a) Infrared radiations b) Ultraviolet radiations ii) Give one use of Infrared radiations. i) Why is white light considered to be polychromatic in nature? [2009] ii) Give the range of the wavelength of those electromagnetic waves which are visible to us. Why are infra red radiations preferred over ordinary visible light for taking photographs in fog? (2007) A particular type of light energy invisible electromagnetic rays, is used to study the structure of crystals. Name these rays and give another important use of these rays. [2007] What is Newton s colour disc? What does the Newton s colour disc experiment establish about the nature of white light? [2006] Give one use each of the electromagnetic radiations given below: [2006] i) Microwaves ii) Ultraviolet radiation iii) Infrared radiation A glass slab is placed over a page on which the word VIBGYOR is printed with each letter in its corresponding colour. [2005] i) Will the image of all the letters be in the same place? ii) If not, state which letter will be raised to the maximum. Give a reason for your answer. Name any four regions of electromagnetic spectrum (other than visible light) in increasing order of wavelength. [2004] ANSWERS: Previous Board Questions: 1) i) The splitting of white light into its constituent colours on passing through a prism is called the dispersion of light. ii) The red colour is scattered the least. 4) i) White light consist of several wavelengths or colours so it is considered to be polychromatic ii) Range of wavelength of electromagnetic waves visible to us is 4000 to 8000 . 8) The image of all the letters of the word VIBGYOR in their corresponding colours will not be at the same place. In glass, red colour has the higher speed than violet colour, so red will be raised to the maximum while violet will be at the bottom and the other colours will be raised in the order II, B, G, Y, O. 116 Universal Tutorials X ICSE Physics Volume 1 of 2

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