Indian Institute of Technology Guwahati (IITG) 2006 JAM Physics  Question Paper
JAM 2006 Physics
Full ques. Paper in attachment
PHYSICS TEST PAPER
Useful Data
1. Speed of light in free space, c = 3 x 10^{8} m s^{1}
2. Plancks constant, h = 6.6 x 10"^{34} J s
3. Electron charge, e = 1.6 x 10^{19} C
4. Electron mass, m_{e} = 9.1 x 10^{31} kg
5. Use e^{3}  20
NOTE: Attempt ALL the 25 questions. Questi ons 115 (objective questions) carry six marks each and questions 1625 (subjective questions) carry twenty one marks each.
Write the answers to the objective questions in the Answer Table for Objective Questions provided on page 12 only.
1. In a crystalline solid, the energy band structure (Ek relation) for an electron of mass m
h^{2}k(2k _{} 3)
is given by E =. The effective mass of the electron in the crystal is
2m
(A) m 2
(B) m
3
_{m}
^{(C) i}
(D) 2 m
2. Two electric dipoles P_{1} and P_{2} are placed at (0, 0, 0) and (1, 0, 0) respectively, with both of them pointing in the +z direction. Without changing the orientations of the dipoles, P_{2} is moved to (0, 2, 0). The ratio of the electrostatic potential energy of the dipoles after moving to that before moving is
(A)
(B)
(C)
(D)
16
1
2
1
4
1
8
J 
K 
Q 
0 
0 
1 
0 
1 
0 
1 
0 
1 
1 
1 
0 
J 
K 
Q 
0 
0 
1 
0 
1 
0 
1 
0 
0 
1 
1 
1 
(B)
At a given point in space the total light wave is composed of three phasors P_{1} = a,
a a _ . q
e ^{1} . The intensity of light at this point is
P_{2} = e^{1} and P_{3} =
^{2} 2 ^{3} 2
(A) 
4 a^{2} cos^{2} 
(B) 
4 a^{2} cos^{4}  
(C) 
a^{2} cos^{2} (q) 
(D) 
4 a^{2} cos^{2} (2 
A small magnetic dipole is kept at the origin in the xy plane. One wire Li is located at z = _ a in the xz plane with a current I flowing in the positive x direction. Another wire L_{2} is at z = + a in yz plane with the same current I as in L_{is} flowing in the positive y direction. The angle <p made by the magnetic dipole with respect to the positive xaxis is
(A) 225
(B) 120
(C) 45
(D) 270
The ratio of the inner radii of two glass tubes of same length is V2. A fluid of viscosity 8.0cP flows through the first tube, and another fluid of viscosity 0.8cP flows through the second one when equal pressure difference is applied across both of them. The ratio of the flow rate in the first tube to that in the second tube is
(A) 
1.6 
(B) 
10 V2 
(C) 
V2 
(D) 
0.4 
The relation between angular frequency o and wave number k for given type of waves is (o^{2} =ak + P k^{3}. The wave number k_{0} for which the phase velocity equals the group velocity is
a  

(A)
(C)
^{(D)}
A neutron of mass m_{n} = 10 kg is moving inside a nucleus. Assume the nucleus to be a
a
10^{}
34
Js and
cubical box of size 10 ^{14} m with impenetrable walls. Take h 1MeV 10^{13} J. An estimate of the energy in MeV of the neutron is
(A)
(B)
(C)
(D)
80 MeV
MeV
8
8 MeV
MeV 80
A springmass system has undamped natural angular frequency o)_{0} = 100 rad s^{1}. The solution x(t) at critical damping is given by x(t) = x_{0}(1 + a>_{0} t) exp(_{0}1), where x_{0} is a constant. The system experiences the maximum damping force at time
9.
0.01 s 0.1 s
0.01 s 0.1 n s
(A)
(B)
(C)
(D)
In an intrinsic semiconductor, the free carrier concentration n (in cm^{} ) varies with temperature T (in Kelvin) as shown in the figure below. The band gap of the
10.
semiconductor is (use Boltzmann constant k_{B} = 8.625 x 10 ^{5} eV K^{1})
(A) 
1.44 
eV 
(B) 
0.72 
eV 
(C) 
1.38 
eV 
(D) 
0.69 
eV 
11. E(x, y, z, t) = A(3 i+ 4 j)exp\i(t  kz)] represents an electromagnetic wave. Possible directions of the fast axis of a quarter wave plate which converts this wave into a circularly polarized wave are
^{(A)} 72^{[ }[ +^{j ] and} 72^{[}1 +^{7 }j]
^{(B)} 72^{[3 }[ +^{4 j] and} 72^{[41 } 3 j]
^{(C)} 72^{[3 }[  4 j ] and 72^{[41} +^{3 j} ]
^{(D)} 72^{[7 [  j] and} 72^{[ }i + ^{7j]}
12. A particle of rest mass m_{0} is moving uniformly in a straight line with relativistic velocity (c, where c is the velocity of light in vacuum and 0 < // < 1. The phase velocity of the de Broglie wave associated with the particle is
(A) 
/c c 
(B) 
( 
(C) 
c 
(D) 
c 
13. Electrons of energy E coming in from x =  ro impinge upon a potential barrier of width 2a and height V_{0} centered at the origin with V_{0} >E, as shown in the figure below. Let
Jim (V_{0}  E ) . k = . In the region  a < x < a, the wave function for the electrons is a
h
linear combination of
k
V0
x
a
(A) e^{kx} and e
(B) e^{lkx} and e
 kx
kx
(C) e^{lkx} and e^{ }lkx
(D) e^{lkx} and e^{kx}
A solid melts into a liquid via first order phase transition. The relationship between the pressure P and the temperature T of the phase transition isP = 2T + P_{0}, where P_{0} is a constant. The entropy change associated with the phase transition is 1.0 J mole^{1} K^{1}. The
ClausiusClapeyron equation for the latent heat is L = T ^{dP} I Av. Here Av = v_{liquid}  v_{solid}
V dT J
is the change in molar volume at the phase transition. The correct statement relating the values of the volumes is
^{(A) v}liquid = vsolid
^{(B) v}liquid = ^{v}solid 1
^{(C) v}liquid = ^{v}solid
2
^{(D) v}liquid = ^{v}solid + ^{2}
The symmetric part of P = I (a 2 b) is
15.
C a^{2} 2 ba 1 _{K}ba 1 b^{2} 2 j a(a 2) b
(A)
(B)
(C)
(D)
2
b
b
2
V^{b(a } 1) J
C a(a 2) b(a 1) b(a 1) b^{2}
b
J
16. Consider a Body Centered Cubic (BCC) crystal with lattice constant a. Determine
(a) the Miller indices for the (1, 0, 0) plane,
[9]
[12]
(b) the number of atoms per unit area in the (1, 1, 1) plane.
= nRT, while during an adiabatic process
17. The equation of state of a gas is P
the gas obeysP V^{Y} = K, where a and K are positive constants. All other symbols have their usual meaning. Find the work done by the gas when it is expanded first isothermally
P
from (P, V) to (Pi, 2V) and then adiabatically from (Pi, 2V) to (, Vj), where P_{1} < P.
18. A conducting sphere of radius R_{A} has a charge Q. It is surrounded by a dielectric spherical shell of inner radius R_{A} and outer radius R_{B} (as shown in the figure below) having electrical permittivity s(r) = s_{0} r .
(a) Find the surface bound charge density at r = R_{A}. [12] (b) Find the total electrostatic energy stored in the dielectric (region B). [9] 
19. For the transistor circuit shown below, evaluate V_{E}, R_{B} and Rc, given I_{C} =1 mA, Vce = 3.8 V, V_{BE} = 0.7 V and V_{cc} = 10 V. Use the approximation I_{c} ~ I_{E}
[21]
20. For the vector field V = xz^{2} i  yz^{2}j + z (x^{2} y^{2} )k ,
(a) calculate the volume integral of the divergence of V over the region defined by
 a < x < a,  b < y < b and 0 < z < c .
_{r} [12]
(b) calculate the flux of V out of the region through the surface at z = c. Hence deduce the net flux through the rest of the boundary of the region. [9]
21. The spherical surface of a planoconvex lens of radius of curvature R = 1m is gently placed on a flat plate. The space between them is filled with a transparent liquid of refractive index 1.55. The refractive indices of the lens and the flat plate are 1.5 and 1.6 respectively. The radius of the sixteenth dark Newtons ring in the reflected light of wavelength X is found to be V5mm.
(a) Determine the wavelength X (in microns) of the light. [12]
(b) Now the transparent liquid is completely removed from the space between the lens and the flat plate. Find the radius (in mm) of the twentieth dark ring in the reflected light after this change. [9]
22. A resistor of 1 kQ and an inductor of 5 mH are connected in series with a battery of emf 4 V through a switch. The switch is closed at time t = 0. In the following, you may use e^{3}  20.
(a) Find the current flowing in the circuit at t = 15 microsecond. [9]
(b) Find the heat dissipated through the resistor during the first 15 microsecond.
[12]
23. A photon of energy Ep_{h} collides with an electron at rest and gets scattered at an angle 60 with respect to the direction of the incident photon. The ratio of the relativistic kinetic energy T of the recoiled electron and the incident photon energy E_{ph} is 0.05.
(a) Determine the wavelength of the incident photon in terms of the Compton
r h }
wavelength X_{c} = , where h, m_{e}, c are Plancks constant, electron rest mass
I ^{m}e^{C})
and velocity of light respectively. [12]
(b) What is the total energy E_{e} of the recoiled electron in units of its rest mass ?
[9]
 3
24. A particle moves in a plane with velocity v = v_{r}r + v_{0}0 such that v_{r} = 4v_{0}. The time
dependence of the magnitude of the velocity  v  = 5t. It is given that r = 1, 0 = 0 and v_{r} > 0 at t = 0. (In the following, you may use e^{3}  20.)
(a) Determine the traj ectory r(0) of the particle. [9]
(b) At what time will 0 become 4 radian? [12]
25. A body of mass 1 kg moves under the influence of a central force, with a potential energy
function V(r) =  ^{exp( 3r /2)} Joule, where r is in meters. It is found to move in a
5r
circular orbit of radius r = 2 m. (In the following, you may use e^{3}  20).
(a) Find its angular momentum L and total energy E. [12]
(b) A piece of mass m_{1} = 0.5 kg breaks off suddenly from the body and begins to fall radially inwards with velocity v = 10 cm s^{1}. What are the values of angular momentum L2 and total energy E2 of the remaining piece, assuming that the potential energy function remains the same? [9]
9
Attachment: 
Earning: Approval pending. 