University of Hyderabad (UoH) 2010 Entrance Exams Other Entrance Exams Ph.D Programme Entrance - Physics - Question Paper

D.    R\n[aP/(RTf/²]

40.    The entropy of a magnetic system changes by an amount AS = -CHAH/T² (where C is a constant) if its temperature is held constant at T and the magnetic field is changed from H to H+AH. The magnetization M of such a system depends on temperature T and field H as

A.    M = CH²/T

B.    M = CT/H

C.    M = C{T/Hf    

D.    M = CH/T

Hint: the change in the Gibbs free energy is given by dG = -SdT - MdH

41.    A system of two energy levels e₀ and (_Cl > e_c) is populated by N particles at temperature T in accordance with the Boltzmann distribution law. The average energy per particle is

A.    e_G + e₁e~(^l~^ey^kB^T

B.    i e₀e~(¹~^ekBT

C.    [e_a + e_ie-(*-^e>)/^fcB^r ]/[l + _e-(¹-^{)/*^r]

D.    [e₀ + e₁e-(^tl-^eV^kBT]/{l-e-~^eV^kBT}

42. A monatomic gas consists of atoms with two internal energy levels: a ground state of degeneracy g_x and an excited state of degeneracy g₂ at an energy e above the ground state (chosen as the zero of energy scale). The specific heat of the gas is

^A* h

B. h_B '^,kBT

2 1 + g2e~!^kBT

3, . g_ig2e²e^(/kBT -Kb '

2 k_BT²(g₂ + _gieBTy

9\92^elkBl k_BT(g₂ + giey

43. Consider an ideal gas consisting of N particles obeying classical statistics. Suppose that the energy of one particle t is proportional to the magnitude of its momentum p, i.e., e = Cp. The partition function of the gas is proportional to

? rp \ 3A^T

k_BT

c ,

N

()

k_BT_j

D. (Ck_BT)^N

44. If in a diffraction experiment X-ray photon of wavevector k gets scattered to the final state with wave vector k' = k + G, where G is a reciprocal lattice vector, the Bragg diffraction condition is given by

A.    k G + G = 0

B.    k-G + G² = 0

C.    k-G = {G-G)/2

D.    k-k = 2(k-G)

45.    If ai ( x + y 4-1); a₂ (i y + i) and a₃ = -( + y - z) are the primitive translation vectors of a cubic lattice of size (lattice parameter) a and x, y, z are the orthogonal unit vectors parallel to the cube edges, the primitive translation vectors bi,b₂,b₃ of the reciprocal lattice are given by

a l*     _x r* 27r .    -* ₀

^{6l =} ~( ^{+ z})^;    1)2 = (z + x)-, b₃ = (.r + y);

^B' ^{=    2 =} ~ ⁼ tl d

^c-* = (y + z)_;    b₂ = -(-z + *); 63 = (-f 4- y);

l 27r    _r 2tt , _s    

"a"^{_y + 2; 2 =} ~(^-2: + )^; 63 =    +

46.    If the atoms vibrating in a lattice at finite temperature are considered to be a collection of N identical harmonic oscillators, as Einstein did, the heat capacity at constant volume for such a solid is given by

A. C_v = Nk_Bx

B.    C_v = Nk_Bx²

e^x -

C.    C_v = Nk_Bx²

(_e* _ 1)2 ^D

where x = hw/k_BT

47. Consider a system of N weakly interacting particles, each of spin | and magnetic moment fi_B, exposed to an external magnetic field H. If the system is in thermal contact with a heat reservoir at temperature T, the mean energy of the system as a function of T and H is given by

A.    Nfi_B sinh(/j,_BH/k_BT)

B.    Nfi_B coth(p,_BH/k_BT)

C.    N/j,_Btanh.~¹(}j,_BH/k_BT)    -

D.    Nfi_BtSLnh(tj,_BH/k_BT)

48.    Which of the following relations is consistent with the London equation curlj = -_47rA2 ^{or a} superconductor, where Al is the London penetration depth.

A.    VB = B/\_l

B.    V²B = B/\_l

C.    V²B = B/Xl

D.    VB = B/X²l

49.    The output V_a of the circuit is

k₂

-ww

A.    V_o = 0

B.    V₀ = (R₂/R₁)V₁

C.    V₀ = (1 + R₂/R₁)V₁

D.    V₀ = -(R₂/RJVr

50. In the following figure, the transistor has f3_dc of 80 and V_CE(_sat) of 0.1 V. R_B is adjusted to get transistor into saturation. The value of Ic(sat) and the corresponding value of Rb are

A.    114 mA and 17 kfi

B.    1.43 mA and 17 kfi

C.    114 mA and 1.7 kfi

D.    1.43 mA and 17.48 kfi

51.    In emitter follower configuration of a transistor

A.    the emitter current follows the collector current and both are in same phase

B.    the collector current follows the emitter current and both are in same phase

C.    the base current follows the emitter current and is in opposite phase

D.    the emitter current follows the base current and both are in same phase

52.    Binary equivalent of (8.2)io is

53.    In a pure germanium the intrinsic concentration of charge (*) at room temperature is 2.5 x 10¹³ cm³. The electron and hole mobilities are given by \i_n = 3800 cm /V-s and n_v 1800 cm²/V-s respectively. The resistivity of the intrinsic germanium is

A.    22.3 fi-cm

B.    66.9 fi-cm

C.    44.6 fi-cm

D.    11.2 O-cm

54.    The change in isospin (A I) in the process A -> p + ir~ is

A.    A/ 0, 1

B.    A/ = |,|

C.    AJ = 0,|

D.    A/ = 1,2

55.    A spin-0 particle A decaying in its rest frame into particles B and C, through strong interaction. Which of the following statement is not true?

A.    0⁺ -> 0+ + 0⁺

B.    0+ -> 0 + 0~

C.    0~->0⁺ + 0

D.    0 - 0 + 0"

where J^p= 0⁺ or 0" representing the standard convention for labeling the spin and intrinsic parity of a particle.

U'S'

56.    Which of the following reactions represents a strong interaction

A.    7r~ -+ p y A -t~ K

B.    p 7T + TT

C.    K~ -) 7T + 7T

D.    p + p > 7T⁺ + 7T

57.    In the nuclear shell model, g⁶0 is a good closed-shell nucleus and has spin parity J^p = 0⁺. What are the predicted J^p values for g⁵0 and I⁷O?

58. A pion at rest decays to a muon and a neutrino. The magnitude of momentum of the outgoing muon is

_D (^mn ~ ^7X1 ji)² _q

'    2m,t.

r

5.9. An experiment is performed to search for the evidence of the particle H through the strong reaction p+p > H + K⁺ + K⁺. The electric charge (Q), Baryon number

(B) and strangeness quantum number (S) of the particle H will be

60.    Let a plane monochromatic wave be totally internally reflected at the interface z = 0 between two dielectrics. Let x - z be the plane of incidence with x along the interface. The planes of constant amplitudes and constant phases in medium 2 are given by

A.    z Ci, x c₂

B.    x + z = Ci, x z = C2

C.    X = Cl, Z C2

D.    X Z = Cl, X + Z = C2

(here ci and c₂ are constants)

61.    The transformation that reduces the wave equation

d²u(x, t) 1 d²u(x, t) dx² c² dt²

3²vl[E , t)

to the form -7 = 0 is given bv

ddT    

A.     = c/(ct + x), T = c/(ct x)

B.     = it + x/c, t = it xjc where i = y/\

C.    ( t + x/c, r = t x/c

D.    f = t + ix/c, t t ix/c where i = y/l

62.    In the domain of anomalous dispersion, the group velocity (v_g), refractive index (n) and speed of light in vacuum (c) obey

A.    v_g > c/n

B.    v_g = c/n    '

C.    v_g < c/n

D.    c/n < v_g < c

63.    The resolving power of a grating of a given width for a given order of diffraction can be increased by

A.    making thinner grooves without changing the groove separation

B.    making thinner grooves and proportionately decreasing the groove separation

C.    making wider grooves without changing the groove separation

D.    making wider grooves and proportionately increasing the groove separation

64. In a Newtons ring experiment, a plano-convex lens with radius of curvature of the convex surface 4.18m is placed on an optically flat surface with its convex surface down. Interference fringes are observed using a travelling microscope and sodium light (A = 589.3 nm). The radius of the tenth dark ring is

65.    Consider a uniformly charged sphere of radius R with total charge q. Let the sphere be coated with a medium with charge density p = a/r (where a > U, r > R). The electric field E outside the charged sphere will be independent of r when

A.    q = 2-KaR²/tQ, E = a/(2e₀) f

B.    q = 2ixaR², E = a/(e₀) f

C.    q iraR², E = a/(2eo)

D.    q = 27raR?₁ E a/(2eo) ?

66.    Consider two infinite current carrying wires rigidly held parallel to the z-axis. The current through the wires is I. The distance between the wires is d. The magnetic field at the points marked P in the three cases shown in the figure below are

(0

2/01 _/.._{x n} /... 4/io/ (i) -ZTV, (^u) 0; (^1U) WZTJV

7T d