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Class 12 Notes 2016 : Physics

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Board Question Paper : March 2015 BOARD QUESTION PAPER : MARCH 2015 Note: i. All questions are compulsory. ii. Neat diagrams must be drawn wherever necessary. iii. Figures to the right indicate full marks. iv. Use of only logarithmic table is allowed. v. All symbols have their usual meaning unless otherwise stated. SECTION I Q.1. Select and write the most appropriate answer from the given alternatives for each subquestion: i. The period of a conical pendulum in terms of its length (l), semivertical angle ( ) and acceleration due to gravity (g) is: (A) 1 l cos 2 g (B) 1 l sin 2 g (C) 4 l cos 4g (D) 4 [7] l tan g ii. The kinetic energy of a rotating body depends upon (A) distribution of mass only. (B) angular speed only. (C) distribution of mass and angular speed. (D) angular acceleration only. iii. If the metal bob of a simple pendulum is replaced by a wooden bob of the same size, then its time period will (A) increase (B) remain same (C) decrease (D) first increase and then decrease iv. The graph between applied force and change in the length of wire within elastic limit is a (A) straight line with positive slope. (B) straight line with negative slope. (C) curve with positive slope. (D) curve with negative slope. v. When longitudinal wave is incident at the boundary of denser medium, then (A) compression reflects as a compression. (B) compression reflects as a rarefaction (C) rarefaction reflects as a compression. (D) longitudinal wave reflects as transverse wave. vi. The dimensions of universal gravitational constant are (B) [L2M1T0] (A) [L1M0T0] (D) [L3M 1T 2] (C) [L 1M1T 2] vii. Two copper spheres of radii 6 cm and 12 cm respectively are suspended in an evacuated enclosure. Each of them are at a temperature 15 C above the surroundings. The ratio of their rate of loss of heat is (A) 2:1 (B) 1 : 4 (C) 1:8 (D) 8 : 1 343 Std. XII Sci.: Perfect Physics I Q.2. Attempt any SIX : [12] i. In circular motion, assuming v r , obtain an expression for the resultant acceleration of a particle in terms of tangential and radial component. ii. Explain why an astronaut in an orbiting satellite has a feeling of weightlessness. iii. State theorem of parallel axes and theorem of perpendicular axes about moment of inertia. iv. State: a. Wein s displacement law, and b. First law of thermodynamics. v. A particle in S.H.M. has a period of 2 seconds and amplitude of 10 cm. Calculate the acceleration when it is at 4 cm from its positive extreme position. vi. The surface tension of water at 0 C is 75.5 dyne/cm. Calculate surface tension of water at 25 C. ( for water = 2.7 10 3/ C) vii. The spin dryer of a washing machine rotating at 15 r.p.s. slows down to 5 r.p.s. after making 50 revolutions. Find its angular acceleration. viii. Calculate the period of revolution of Jupiter around the Sun. The ratio of the radius of Jupiter s orbit to that of the Earth s orbit is 5. (Period of revolution of the Earth is 1 year) Q.3. Attempt any THREE i. Derive an expression for excess pressure inside a drop of liquid. ii. Explain what is Doppler effect in sound and state its any four applications. iii. Calculate the average molecular kinetic energy: a. per kilomole, b. per kilogram, of oxygen at 27 C. (R = 8320 J/k mole K, Avogadro s number = 6.03 1026 molecules/K mole) iv. A uniform steel rod of 5 mm2 cross section is heated from 0 C to 25 C. Calculate the force which must be exerted to prevent it from expanding. Also calculate strain. ( for steel = 12 10 6/ C and for steel = 20 1010 N/m2) Q.4. A. What are forced vibrations and resonance? Show that only odd harmonics are present in an air column vibrating in a pipe closed at one end. A stretched wire emits a fundamental note of frequency 256 Hz. Keeping the stretching force constant and reducing the length of wire by 10 cm, the frequency becomes 320 Hz. Calculate the original length of wire. OR Obtain an expression for potential energy of a particle performing simple harmonic motion. Hence evaluate the potential energy a. at mean position and b. at extreme position. A horizontal disc is freely rotating about a transverse axis passing through its centre at the rate of 100 revolutions per minute. A 20 gram blob of wax falls on the disc and sticks to the disc at a distance of 5 cm from its axis. Moment of intertia of the disc about its axis passing through its centre of mass is 2 10 4 kg m2. Calculate the new frequency of rotation of the disc. [9] B. A. B. 344 [7] [7] Board Question Paper : October 2015 BOARD QUESTION PAPER : OCTOBER 2015 Note: i. All questions are compulsory. ii. Neat diagrams must be drawn wherever necessary. iii. Figures to the right indicate full marks. iv. Use of only logarithmic table is allowed. v. All symbols have their usual meaning unless otherwise stated. SECTION I Q.1. A. State an expression for the moment of intertia of a solid uniform disc, rotating about an axis passing through its centre, perpendicular to its plane. Hence derive an expression for the moment of inertia and radius of gyration: i. about a tangent in the plane of the disc, and ii. about a tangent perpendicular to the plane of the disc. B. In a set, 21 turning forks are arranged in a series of decreasing frequencies. Each tuning fork produces 4 beats per second with the preceding fork. If the first fork is an octave of the last fork, find the frequencies of the first and tenth fork. A. B. [7] OR Discuss the composition of two S.H.M.s along the same path having same period. Find the resultant amplitude and intial phase. A sonometer wire is in unison with a tuning fork of frequency 125 Hz when it is stretched by a weight. When the weight is completely immersed in water, 8 beats are heard per second. Find the specific gravity of the material of the weight. Q.2. Select and write the most appropriate answer from the given alternatives for each sub-question : i. Which of the following substances is ductile? (A) Glass (B) High carbon steel (C) Steel (D) Copper ii. A seconds pendulum is suspended in an elevator moving with constant speed in downward direction. The periodic time (T) of that pendulum is _______. (A) less than two seconds (B) equal to two seconds (C) greater than two seconds (D) very much greater than two seconds iv. The equation of a progressive wave is y = 7 sin (4t 0.02x), where x and y are in cms and time t in seconds. The maximum velocity of a particle is _______. (A) 28 cm/s (B) 32 cm/s (C) 49 cm/s (D) 112 cm/s v. The dimensions of emissive power are (A) [M1L 2T 3] (C) [M1L0T 3] [7] Angle of contact for the pair of pure water with clean glass is _______. (A) acute (B) obtuse (C) 90 (D) 0 iii. [7] (B) (D) [M1L2T 3] [M1L0T 2] 345 Std. XII Sci.: Perfect Physics I vi. (A) (C) vii. 2E , then the energy E is _______. 3V rotational kinetic inversely proportional to pressure The pressure (P) of an ideal gas having volume (V) is translational kinetic vibrational kinetic (B) (D) The fundamental frequency of transverse vibration of a stretched string of radius r is proportional to _______. (A) r 2 (B) r 1 (C) r 1 2 (D) r2 Q.3. Attempt any SIX: i. Draw a neat labelled diagram of conical pendulum. State the expression for its periodic time in terms of length. ii. A raindrop of diameter 4 mm is about to fall on the ground. Calculate the pressure inside the raindrop. [Surface tension of water T = 0 072 N/m, atmospheric pressure = 1 013 105 N/m2] iii. [12] Discuss the weightlessness experienced by an astronaut in an orbiting satellite. The periodic time of a linear harmonic oscillator is 2 second, with maximum displacement of 1 cm. If the particle starts from extreme position, find the displacement of the particle after seconds. 3 v. State and prove : Law of conservation of angular momentum. vi. A pinhole is made in a hollow sphere of radius 5 cm whose inner wall is at temperature 727 C. Find the power radiated per unit area. [Stefan s constant = 5 7 10 8J/m2s K4, emissivity (e) = 0 2] vii. Draw a neat labelled diagram showing forces acting on the meniscus of water in a capillary tube. viii. Compute the temperature at which the r.m.s. speed of nitrogen molecules is 832 m/s. [Universal gas constant, R = 8320 J/k mole K, molecular weight of nitrogen = 28.] iv. Q.4. Attempt any THREE: i. Discuss the behaviour of wire under increasing load. ii. Determine the binding energy of satellite of mass 1000 kg revolving in a circular orbit around the Earth when it is close to the surface of Earth. Hence find kinetic energy and potential energy of the satellite. [Mass of Earth = 6 1024 kg, radius of Earth = 6400 km; gravitational constant G = 6 67 10 11 Nm2/kg2] iii. Show that all harmonics are present on a stretched string between two rigid supports. iv. A stone of mass 100 g attached to a string of length 50 cm is whirled in a vertical circle by giving velocity at lowest point as 7 m/s. Find the velocity at the highest point. [Acceleration due to gravity = 9 8 m/s2] 346 [9] Board Question Paper : March 2016 BOARD QUESTION PAPER : MARCH 2016 Note: i. All questions are compulsory. ii. Neat diagrams must be drawn wherever necessary. iii. Figures to the right indicate full marks. iv. Use of only logarithmic table is allowed. v. All symbols have their usual meaning unless otherwise stated. vi. Answers to both sections must be written in the same answerbook. vii. Answer to every question must be written on a new page. SECTION I Q.1. Attempt any SIX : i. ii. iii. [12] In U.C.M. (Uniform Circular Motion), prove the relation v r , where symbols have their usual meanings. Derive an expression for critical velocity of a satellite revolving around the earth in a circular orbit. K2 1 Obtain an expression for total kinetic energy of a rolling body in the form MV2 1 2 . 2 R iv. v. Define emissive power and coeficient of emission of a body . A coin kept at a distance of 5 cm from the centre of a turntable of radius 1.5 m just begins to slip when the turnable rotates at a speed of 90 r.p.m. Calculate the coefficient of static friction between the coin and the turntable. [g = 9.8 m/s2]. vi. The fundamental frequency of an air column in a pipe closed at one end is in unison with the third overtone of an open pipe. Calculate the ratio of lengths of their air columns. vii. A particle performing linear S.H.M. has a period of 6.28 seconds and a pathlength of 20 cm. What is the velocity when its displacement is 6 cm from mean position? viii. The energy of the free surface of a liquid drop is 5 times the surface tension of the liquid. Find the diameter of the drop in C.G.S. system. Q.2. Select and write the most appropriate answer from the given alternatives for each subquestion: i. A particle rotates in U.C.M. with tangential velocity v along a horizontal circle of diameter D . Total angular displacement of the particle in time t is _______ v (A) vt (B) t D vt 2vt (D) (C) 2D D ii. Two springs of force constants K1 and K2 (K1 > K2) are stretched by same force. If W1 and W2 be the work done stretching the springs then _______ (A) W1 = W2 (B) W1 < W2 (D) W1 = W2 = 0 (C) W1 > W2 iii. [7] A and B are two steel wires and the radius of A is twice that of B. If they are stretched by the same load, then the stress on B is _______. (A) four times that of A (B) two times that of A (C) three times that of A (D) same as that of A 347 Std. XII Sci.: Perfect Physics I iv. If sound waves are reflected from surface of denser medium, there is phase change of _______ (A) 0 rad (B) rad 4 rad (D) rad (C) 2 v. A sonometer wire vibrates with frequency n1 in air under suitable load of specific gravity . When the load is immersed in water, the frequency of vibration of wire n2 will be _______ 1 1 (B) n1 (A) n1 (D) n1 (C) n1 1 1 vi. For polyatomic molecules having f vibrational modes, the ratio of two specific heats, _______. 1 f (A) 2 f 4 f (C) 3 f vii. Q.3. A. B. A. B. (B) (D) CP is CV 2 f 3 f 5 f 4 f A body of moment of inertia 5 kgm2 rotating with an angular velocity 6 rad/s has the same kinetic energy as a mass of 20 kg moving with a velocity of _______. (A) 5 m/s (B) 4 m/s (C) 3 m/s (D) 2 m/s Define linear S.H.M. Show that S.H.M. is a projection of U.C.M. on any diameter. A metal sphere cools at the rate of 4 C/min. when its temperature is 50 C. Find its rate of cooling at 45 C if the temperature of surroundings is 25 C OR Explain analytically how the stationary waves are formed. Hence show that the distance between node and adjacent antinode is . 4 A set of 48 tuning forks is arranged in a series of descending frequencies such that each fork gives 4 beats per second with preceding one. The frequency of first fork is 1.5 times the frequency of the last fork, find the frequency of the first and 42nd tuning fork. Q.4. Attempt any THREE i. What is the decrease in weight of a body of mass 600 kg when it is taken in a mine of depth 5000 m? [Radius of earth = 6400 km, g = 9.8 m/s2] ii. State and prove theorem of parallel axes about moment of inertia. iii. Derive Laplace s law for spherical membrane of bubble due to surface tension. iv. A steel wire having cross sectional area 1.5 mm2 when stretched by a load produces a lateral strain 1.5 10 5. Calculate the mass attached to the wire. (Ysteel = 2 1011 N/m2, Poisson s ratio = 0.291, g = 9.8 m/s2) 348 [7] [7] [9]

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