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IIT JAM 2013

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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 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 1 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES IIT JAM (PHYSICS) 2013 Q1. 0 1 1 The inverse of the matrix M 0 0 1 is 1 0 0 (a) M I (b) M 2 I (c) I M 2 (d) I M (c) (d) 2 where I is the identity matrix. Q2. The value of (a) 0 Q3. i i , where i 1, is (b) 1 2 2 2 x2 x , x 0 . Which one of A particle is released at x 1 in a force field F x x2 2 e the following statements is FALSE? (a) F x is conservative (b) The angular momentum of the particle about the origin is constant (c) The particle moves towards x 2 (d) The particle moves towards the origin 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 2 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q4. 2abxt a 2 x 2 b 2 t 2 A traveling pulse is given by f x, t A exp c2 , where A, a, b and c are positive constants of appropriate dimensions. The speed of the pulse is (a) Q5. b a (b) (c) cb a (d) b 2a If the dimensions of mass, length, time and charge are M , L, T and C respectively, the dimensions of the magnetic induction field B is (a) ML2T 1C 1 Q6. 2b a (b) MT 1C 1 (c) L2T 1C (d) L 1T 1C A blackbody at temperature T emits radiation at a peak wavelength . If the temperature of the blackbody becomes 4T , the new peak wavelength is (a) Q7. 1 256 (b) 1 64 (c) 1 16 (d) 1 4 Let N MB , N BE , N FD denote the number of ways in which two particles can be distributed in two energy states according to Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics respectively. Then N MB : N BE : N FD is (a) 4 : 3 : 1 Q8. Electric (b) 4 : 2 : 3 field component of an (c) 4 : 3 : 3 electromagnetic (d) 4 : 3 : 2 radiation varies with time as E a cos 0 t sin t cos 0 t , where a is a constant and the values of and 0 are 1 1015 s 1 and 5 1015 s 1 respectively. This radiation falls on a metal of work function 2eV . The maximum kinetic energy (in eV ) of photoelectrons is (a) 0.64 (b) 1.30 (c) 1.70 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) 1.95 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 Q9. The fraction of volume unoccupied in the unit cell of the body centered cubic lattice is (a) Q10. 8 3 8 (b) 3 8 (c) 6 2 6 (d) 3 2 For an ideal op-amp circuit given below, the dc gain and the cut off frequency respectively are 1 k 1 F 2 10 k 1 k (a) 1 and 1 kHz (b) 1 and 100 Hz (c) 11 and 1 kHz 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) 11 and 100 Hz 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 Fill in the blanks questions Q11. The solution of the differential equation dz x, y xz x, y dx yz x, y dy 0 is _____ Q12. Given that f 1 1, f 1 1, and f " 1 1, the value of f 1 2 is Q13. Two tubes A and B are connected through another tube C . A mercury manometer is connected between B and C (see figure). The diameters of B and C are 0.04 m and 0.01 m, respectively. An incompressible fluid of density 1.0 103 kgm-3 enters A and leaves B with a constant speed 0.2 ms-1. If the density of mercury is 13.6 10 3 kgm-3, the height h of the mercury column in the manometer is (Take acceleration due to gravity g 10 ms-2) A B C h Q14. The path of a particle of mass m , moving under the influence of a central force, in plane polar coordinates is given by r r0 e k , where r0 and k are positive constants of appropriate dimensions. The angular momentum of the particle is L and its total energy is zero. The potential energy functions V r , in terms of m, L and k is ______________ Q15. The dimensions of a thin convex lens of refractive index n are shown in the figure. The radius of curvature of the lens in terms of n, h and (where, h ) is h h 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 5 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q16. A charged particle of mass m , charge q and constant velocity v enters a uniform x , B0 0 , at an angle to the direction of magnetic field. Find magnetic field B B0 e the angle , if in one revolution of the helical motion, the particle advances along the direction of the magnetic field a distance equal to the radius of the helical path. Q17. Two thermally isolated identical systems have heat capacities which vary as C v T 3 (where 0 ). Initially one system is at 300 K and the other at 400 K. The systems are then brought into thermal contact and the combined system is allowed to reach thermal equilibrium. The final temperature of the combined system is _________ Q18. A beam of X-rays of wavelength 0.2 nm is incident on a free electron and gets scattered in a direction with respect to the direction of the incident radiation resulting in maximum wavelength shift. The percentage energy loss of the incident radiation is _____________ Q19. A free particle of mass m is confined to a region of length L . The de Broglie wave associated with the particle is sinusoidal in nature as given in the figure. The energy of the particle is 0 L/3 Q20. 2L / 3 L A variable power supply (5 V 20 V) is connected to a Zener diode specified by a breakdown voltage of 10 V (see figure). The ratio of the maximum power to the minimum power dissipated across the load resistor is 500 5V 20V 1 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 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 Descriptive questions Q21. Apply Gauss divergence theorem to the gravitational field due to a spherical object of mass M and uniform density located at the origin. Obtain Gauss s law for gravitation (analogous to the Gauss law in electrostatics) in integral and differential forms. Q22. A thin annular disc of inner and outer radii a and b a b respectively has uniform mass density s and is placed in the xoy -plane such that its axis lies along the z-axis. Determine the gravitational force due to the disc on a particle of mass m located on the z-axis at a distance z from the origin. If the particle is released at z, such that z a, b describe the nature of motion of the particle. Q23. A concentric spherical volume of inner radius a and outer radius b is filled with a material of finite conductivity specified by r A , r2 where A is a positive constant of appropriate dimensions. The outer surface is grounded and the inner surface is maintained at a potential V0 . Calculate the resistance of this configuration. V0 a b Q24. A conducting solid sphere of radius a , carrying a charge q is kept in a dielectric of dielectric constant k , such that half the sphere is surrounded by the dielectric as shown in figure. Find the surface charge densities in the upper and lower hemispherical surfaces. q a 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 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 Q25. A particle of mass m is subjected to a potential V x ax 2 , x , where a is a positive constant of appropriate dimensions. Using the relation x p , estimate the 2 minimum energy of the particle. Q26. A hollow cylinder (closed at both ends) with adiabatic walls is divided into n equal cells C1 , C 2 ,....C n using discs D1 , D2 , ....Dn 1 (see figure). The discs can slide freely without friction. The first D1 is adiabatic and the remaining discs are diathermal (thermally conducting). Each cell contains one mole of ideal monoatomic gas. Let the initial pressure, volume and temperature of each cell be P0 ,V0 and T0 , respectively. The gas in cell C1 (first cell) is heated slowly until the temperature of the gas in cell C n (last cell) reaches final equilibrium temperature 4T0 . Find the volume of the first cell in terms of the number of cells n and the initial volume V0 . D1 D2 D3 C1 C2 C3 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 Dn 1 Cn 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 Q27. A spaceship S1 leaves the Earth along the positive x -direction. Another spaceship S 2 also leaves the Earth along the direction which makes an angle 60o with x - axis. The speeds of S1 and S 2 are measured as 0.6c and 0.9c respectively by an observer on the Earth. Find the speed of S 2 as measured by an observer in S1 . y V 2 0 .9 c S2 x O 60 o V1 0.6c S1 Eearth Q28. For the given circuit, calculate the input impedance, output impedance and voltage gain. Use 200, VBE 0.7 V and re 26 mV . IE 20V 12k 2.2 k 10 F 1 F 1 k 3.9 k 5k 1 k 50 V 20 F 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 9 fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Q29. The mass density of a disc of mass m and radius R varies as r r 0 1 for 0 r R R 0 for r R Find the moment of inertia of the disc about the axis perpendicular to the plane of the disc and passing through the centre of the disc in terms of m and R . Q30. The speed of sound propagation in air as a function of temperature T is given by v T , where is a constant of appropriate dimensions. Calculate the time taken for a sound wave to travel a distance L between two points A and B , if the air temperature between the points varies linearly from T1 to T2 . 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

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