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IIT JAM 2014

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Brijmohan
Banaras Hindu University (BHU), Varanasi
PhD Condensed matter Physics
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fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES IIT-JAM 2014 PART-1: OBJECTIVE QUESTIONS 1. 2. , b 2i 3 and c For vectors a j k j 5k j k , the vector product a b c is (a) in the same direction as c (b) in the direction opposite to c (c) in the same direction as b (d) in the direction opposite to b A particle of mass m carrying charge q is moving in a circle in a magnetic field B. According to Bohr s model, the energy of the particle in the nth level is (a) 3. 1 n2 hqB m hqB (b) n m hqB (c) n 2 m hqB (d) n 4 m A conducting slab of copper PQRS is kept on the xy plane in a uniform magnetic field along x-axis as indicted in the figure. Z A steady current I flows through the S cross section of the slab along the y-axis. The direction of the electric Q P field inside the slab, arising due to the applied magnetic field is along R I Y B X the (a) negative Y direction (c) negative Z direction 4. (b) positive Y direction (d) positive Z direction A collimated beam of light of diameter 1 mm is propagating along the x-axis. The beam is to be expanded to a collimated beam of diameter 10 mm using a combination of two convex lenses. A lens of focal length of 50 mm and another lens with focal length F are to be kept at a distance d between them. The values of F and d respectively, are (a) 450 mm and 10 mm (c) 550 mm and 600 mm 5. (b) 400 mm and 500 mm (d) 500 mm and 550 mm Octal equivalent of decimal number 47810 is (a) 7368 (b) 6738 (c) 637 8 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com (d) 3678 Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 1 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES 6. A spherical ball of ice has radius R0 and is rotating with an angular speed about an axis passing through its centre. At time t 0, it starts acquiring mass because the moisture (at rest) around it starts to freeze on it uniformly. As a result its radius increases as R t R0 t , where is a constant. The curve which best describes its angular speed with time is (a) (b) t t (c) (d) t 7. t In 1- dimension, an ensemble of N classical particles has energy of the form 2 P 1 E x kx 2 . The average internal energy of the system at temperature T is 2m 2 (a) 8. 3 Nk B T 2 (b) 1 Nk B T 2 (c) 3Nk BT (d) Nk BT In a photoelectric effect experiment, ultraviolet light of wavelength 320 nm falls on the photocathode with work function of 2.1 eV. The stopping potential should be close to (a) 1.8 V 9. (b) 1.6 V (c) 2.2 V (d) 2.4V In an ideal operational amplifier depicted below, the potential at node A is 5 k A 25 k _ 5V IV (a) 1 V (b) 0 V (c) 5 V Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com (d) 25 V Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 2 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES 10. To operate a npn transistor in active region, its emitter-base and collector- base junction respectively, should be (a) forward biased and reversed biased (b) forward biased and forward biased (c) reversed biased and forward biased (d) reversed biased and reversed biased 11. The value of r n sin n for r = 0.5 and n 0 (a) 12. 1 3 (b) 2 3 is 3 3 2 (c) (d) 3 In a parallel plate capacitor the distance between the plates is 10 cm. Two dielectric slabs of thickness 5 cm each and dielectric constants K 1 2 and K 2 4 respectively, are inserted between the plates. A potential of 100 V is applied across the capacitor as shown in the figure. The value of the K2 4 10 cm 100 V K1 2 net bound surface charge density at the interface of the two dielectrics is (a) 13. 2000 0 3 (b) 1000 0 3 (c) 250 0 (d) 2000 0 3 The electric fields of two light sources with nearby frequencies 1 and 2 , and wave vectors k1 and k 2 , are expressed as E1 E10 i e i k1 z 1t and E 2 E 20 i e i k2 z 2t , respectively. The interference pattern on the screen is photographed at t t 0 ; denote k1 k 2 z 1 2 t 0 by . For this pattern (a) a bright fringe will be obtained for cos 1 (b) a bright fringe intensity is given by E10 E 20 2 2 (c) a dark fringe will be obtained for cos 1 (d) a drak fringe intensity is given by E10 E 20 2 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 3 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES 14. A solid metallic cube of heat capacity S is at temperature 300 K. It is brought in contact with a reservoir at 600 K. If the heat transfer takes place only between the reservoir and the cube, the entropy change of the universe after reaching the thermal equilibrium is (a) 0.69 S 15. (b) 0.54 S (c) 0.27 S (d) 0.19 S over the closed y If the surface integral of the field A x, y, z 2 x i j 3 z k surface of an arbitrary unit sphere is to be zero, then the relationship between , and 16. (a) / 6 0 (b) / 3 / 6 / 2 0 (c) / 2 / 3 0 is (d) 2 / 1 / 3 / 0 The moment of inertia of a disc about one of its diameters is I M . The mass per unit area of the disc is proportional to the distance from its centre. If the radius of the disc is R and its mass is M, the value of I M is (a) 17. 1 MR 2 2 (b) 2 MR 2 5 (c) 3 MR 2 10 (d) 3 MR 2 5 A rigid uniform horizontal wire PQ of mass M, pivoted at P, carries a constant current I. It rotates with a constant angular speed in a Q P uniform vertical magnetic field B. If the current were switched off, the angular acceleration of the wire, in terms of B, M and I would be (a) 0 18. (b) 2 BI 3M (c) 3BI 2M (d) BI M Two points N and S are located in the northern and southern hemisphere, respectively, on the same longitude. Projectiles P and Q are fired from N and S, respectively, towards each other. Which of the following options is correct for the projectiles as they approach the equator? (a) Both P and Q will move towards the east (b) Both P and Q will move towards the west (c) P will move towards the east and Q towards the west (d) P will move towards the west and Q towards the east Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 4 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES 19. Two particles A and B of mass m and one particle C of mass M are kept on the x axis in . Consequently there are two collisions, the order ABC. Particle A is given a velocity vi both of which are completely inelastic. If the net energy loss because of these collisions is 7 of the initial energy, the value of M is (ignore frictional losses) 8 (a) 8 m 20. The line integral (b) 6 m (c) 4 m (d) 2 m of a vector field A d l A x, y 12 yi x j , where r 2 x 2 y 2 , is r taken around a square (see figure) of side unit length and centered at x0 , y0 with x0 1 1 and y0 . If the value of the integral is L, then 2 2 y x0 , y0 x (a) L depends on x0 , y0 (b) L is independent of x0 , y 0 and its value is -1 (c) L is independent of x0 , y 0 and its value is 0 (d) L is independent of x0 , y 0 and its value is 2 21. Diamond lattice can be considered as a combination of two fcc lattice displaced along the body diagonal by one quarter of its length. There are eight atoms per unit cell. The packing fraction of the diamond structure is (a) 0.48 22. (b) 0.74 (c) 0.34 (d) 0.68 Thermal neutrons (energy = 300 k B 0.025 eV) are sometimes used for structural determination of materials. The typical lattice spacing of a material for which these can be used is (a) 0.01 nm (b) 0.05 nm (c) 0.1 nm Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com (d) 0.15 nm Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 5 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES 23. What is the maximum height above the dashed line attained by the water stream A coming out at B from a thin tube of the h water tank assembly shown in the L figure? Assume h = 10 m, L = 2 m and B y 0 30 . (a) 10 m 24. (b) 2 m (c) 1.2 m (d) 3.2 m A steady current in a straight conducting wire produces a surface charge on it. Let E out and Ein be the magnitudes of the electric fields just outside and just inside the wire, respectively. Which of the following statements is true for these fields? (a) E out is always greater than Ein (b) E out is always smaller than Ein (c) E out could be greater or smaller than Ein (d) E out is equal to Ein 25. A small charged spherical shell of radius 0.01 m is at a potential of 30 V. The electrostatic energy of the shell is (a) 10 10 J 26. (b) 5 10 10 J (c) 5 10 9 J (d) 10 9 J At an instant shown, three point masses m, 2m and 3m rest on a horizontal surface, and are at the vertices of an equilateral triangle 3m of unit side length. Assuming that G is the gravitational constant, the magnitude and direction of the torque on the mass 3m, m about the point O, at that instant is O 2m (a) Zero (b) 3 G 3m 2 , going into the paper 2 (c) 3G 3m 2 , coming out of the paper (d) 3 G 3m 2 , going into the paper 4 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 6 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES 27. A sine wave of 5 V amplitude is applied at Vin the input of the circuit shown in the figure. Which of the following Vout 1 k waveforms represents the output most closely? 3V 5V 5V (a) (b) -3V -5V (c) 3V (d) 3V -3V -5V 28. 1011 binary input have been applied at X 3 X 2 X 1 X 0 input in the shown logic circuit made of XOR gates. The binary output Y3Y2Y1Y0 of the circuit will be X3 Y3 X2 X1 29. Y1 X0 (a) 1101 Y2 Y0 (b) 1010 (c) 1111 (d) 0101 A ring of radius R carries a linear charge density . It is rotating with angular speed . The magnetic field at its center is (a) 3 0 2 (b) 0 2 (c) 0 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com (d) 0 Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 7 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES 30. A stationary source (see figure below) emits sound waves of frequency f towards a wall. If an observer Source Wall moving with speed u in a direction perpendicular to 30 9 f at the instant 8 30 the wall, measures a frequency f Observer u shown, then u is related to the speed of sound Vs as (a) Vs 31. (b) Vs / 2 (c) Vs / 4 (d) Vs / 8 A real gas has specific volume v at temperature T. Its coefficient of volume expansion and isothermal compressibility are and kT , respectively. Its molar specific heat at constant pressure C p and molar specific heat at constant volume C v are related as (a) C p C v R (c) C p C v 32. (b) C p C v Tv 2 kT Tv kT (d) C p C v Two frames, O and O , are in relative motion as shown. O c/2 is moving with speed c/2, where c is the speed of light. In frame O, two separate events occur at x1 , t1 and x 2 , t 2 . O O x In frame O , these events occur simultaneously. The value of x2 x1 / t 2 t1 is (a) c / 4 33. (b) c / 2 (c) 2c (d) c White light is incident on a grating G1 with groove density 600 lines/mm and width 50 mm. A small portion of the diffracted light is incident on another grating G 2 with groove density 1800 lines/mm and width 15 mm. The resolving power of the combined system is (a) 3 10 3 (b) 57 10 3 (c) 81 10 7 Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com (d) 108 10 5 Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 8 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES 34. Four particles of mass m each are inside a two dimensional square box of side L. If each state obtained from the solution of the Schrodinger equation is occupied by only one h2 particle, the minimum energy of the system in units of is mL2 (a) 2 35. 5 2 (b) (c) 11 2 (d) 25 4 At atmospheric pressure 10 5 Pa , aluminium melts at 550 K. As it melts, its density decreases from 3 10 3 kg/m 3 to 2.9 10 3 kg/m 3 . Latent heat of fusion of aluminium is 24 10 3 J/kg. The melting point of aluminium at a pressure of 10 7 Pa is closest to (a) 551.3 K (b) 552.6 K (c) 558.7 K Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com (d) 547.4 K Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 9 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES PART II: Descriptive Questions 36. Find the solution of the differential equation y 0 2 and 37. dy dx d2y dy 5 0 with the boundary condition 2 dx dx 2, giving all steps clearly. Find the value of x where y 0. x 0 The electric field in an electromagnetic (EM) wave is E 6 i sin 2 10 6 z 3 1014 t . What is the intensity of the EM wave and the number of photons per second falling on the unit area of a perfectly reflecting screen kept perpendicular to the direction of propagation? When a photon in this beam is reflected from the screen, what is the impulse it imparts to the screen? Use this to find the pressure exerted by the EM wave on the screen. 38. A uniform rod of mass m and length l is hinged at O one of its ends O and is hanging vertically. It is hit at its midpoint with a very short duration impulse J so that it starts rotating about O. Find the magnitude J and direction of the horizontal impulse that O applies on the rod when it is hit. 39. An easy derivation of PV constant for an ideal gas undergoing an adiabatic process: Consider P and V as the basic variables of an ideal gas and write the heat exchanged dQ in terms of dV and dP. Next, using the definition of C P and CV in the expression for dQ, obtain a differential equation relating P and V for an adiabatic process and solve it to get the desired relationship. Derivation SHOULD NOT use the first law of f f thermodynamics. [For a function f x, y the differential df dx y dy] . x y x Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 10 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES 40. A shown in the figure below, an unpolarised beam of light of wavelength 500 nm is incident on a linear polariser at AF with vertical polarization. The light beam then passes through a wave plate BE (half wave or quarter wave plate) of thickness 1.00125 mm and gets reflected from a mirror CD. The reflected light is indicated by the dashed line (DEF) in the diagram. The ordinary and extraordinary refractive indices for the material of the wave plate are 1.658 and 1.558, respectively. Light is incident normally on all surfaces. A B C F E D Linear polarizer Wave plate Plane mirror (a) What is the polarisation of the beam at C? (b) What is the polarisation of the beam at E and F? 41. A standing wave of light is formed between two mirrors and a beam of atoms is incident on it normally (see figure below) from the left. On the right side, atoms are detected in the direction of the beam and also at an angle as shown in the figure. This is due to material waves of atoms diffracted by the standing wave that acts like a grating; the slit width of this grating is given by the distance between two maxima of the light intensity. If the atomic beam is made of atoms of mass m moving with speed v and the light wave has wavelength L , find the smallest angle by using the diffraction condition. Atomic beam Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 11 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES 42. According to Wien s theory of black body radiation, the spectral energy density in a blackbody cavity at temperature T is given as uT d / T e d c 3 5 where and are constants and c is the speed of light. Further, the intensity of uT C radiation coming out of the cavity is , where uT u T d is the total energy 4 0 density of radiation. Given that Stefan-Boltzmann constant 5.67 10 8 Wm 2 K 4 and 3 max T 2.90 10 m.K , find the values of and . The value of integral x 3e x dx 6. 0 43. A horizontal rod of proper length L moves with uniform speed V 0 along the x-axis of a coordinate frame. A ground observer measures the position coordinates of its two ends at two different time, with time difference t 0. The observer finds that the difference between the two coordinates is L. Calculate t in terms of L, V and the speed of light c. If measured correctly, what would have been the length of the rod in the ground frame? Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 12

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