LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM 2016/PHYSICS/2.pdfthe line passing through the centre and parallel to the length of two parallel plates with a spacing of 0.1 m. The plates

1

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Instructions

1. This test paper has a total of 50 questions. The entire question paper is divided in two sections, A and B. All sections are

compulsory. Question in each section are different type.

2. Question 1 to 30 carrying 2 marks & 31 to 50 carrying 4 marks each.

3. Read the Questions carefully and mark your appropriate response to the OMR sheet.

4. There is Negative marking of 1/4 for each wrong answer.

5. Mark the response by Black or Blue Ball Pen only.

6. Any other belongings like Book/ Notes / Electronic device etc are not permitted in the examination hall.

7. Submit your answer sheet (OMR Sheet) to the invigilator before leaving the examination hall.

Date: 26/Nov/16, M.M:200 Timing: 2:00 H

BOOKLET CODE SUBJECT CODE

PHYSICAL SCIENCE TEST SERIES # 2 Thermal, Statistics & Electromagnetic Theory

Student Name: ____________________________

Father’s Name: ____________________________

Exam Centre Name: _______________________

Mobile No.:_________________________________

UGC POINT ACADEMY LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM

05 A

2



1. An electric field is expressed as ˆ ˆ3 5E i j in the observer frame. What is the electric field in a

reference frame moving with velocity 7ˆ ˆ(7 9 ) 10 /seci j m relative to the observers?

(1) ˆ ˆ3 5i j (2) ˆ ˆ3.1 5.1i j

(3) ˆ ˆ3 5i j (4) ˆ ˆ3.1 5.1i j

2. Consider a capacitor placed in free space, consisting of two concentric circular parallel plates of radii

r . The separation z between the plates oscillates with a constant frequency , i.e.,

0 1( ) cosz t z z t . Here 0z and 1 0( )z z are constants. The separation ( )( )z t r is varried in

such the way that the voltage 0V across the capacitor remains constant. Find the displacement current

between the plates through a concentric circle of radius /2r

(1) 2

0 0 1

2

0 1

sin

4( cos )

V z r t

z z t

(2)

2

0 0 1

2

0 1

sin

4( cos )

V z r t

z z t

(3) 2

0 0 0

2

1 0

sin

4( cos )

V z r t

z z t

(4)

2

0 0 0

1 0

sin

4( sin )

V z r t

z z t

3. A long straight solenoid of radii R and n turns per unit length carriers a current I t , where is a

constant, t is the time and remains finite. The axis of solenoid is along the z -axis. Find the electric

field and pointing vector inside the solenoid.

(1) 2

00 ,

2

n rtn r

(2)

2 2 2

0 0,2 2

n rt n rt

(3) 2

2 2 00 ,

2

n rtn r

(4)

2 2 2 2 2

0 0,2 2

n r n r t

4. A charge of magnitude 109.8 10 c and mass 42 10 kg is suspended through a silk thread along

the line passing through the centre and parallel to the length of two parallel plates with a spacing of

0.1 m. The plates are connected to a voltage source of 2000V (take 29.8g ms ). Find the angle

that the tread makes with the vertical when charge is in equilibrium.

(1) 2

(2)

3

2

(3)

6

(4)

4

5. At normal incidence a bema of light propagating in the vaccum reflects off an interface with a

medium of refractive index 3.0n . The fraction of energy reflected R is given by2

1

1

nR

n

.

If the fractional error in the value of n is 1% the fractional error in the estimation of R is

(1) 0.5% (2) 1% (3) 1.5% (4) 2%

6. Two electric dipoles 1P and 2P are placed at (0, 0,) and (1, 0, 0) respectively, with both of them

pointing in z direction without changing the orientations of the dipoles, 2P is moved to (0, 3, 0).

The ratio of electrostatic potential energy of the dipoles after moving to that before moving is

(1) 1

16 (2)

1

2 (3)

1

27 (4)

1

8

7. An infinitely long straight conductor and a rectangular frame made of conducting wire are kept in

such a way that the two long sides of the frame are parallel to the straight conductor. The distance

between the conductor and the two long sides of the frame are 1l and 2 2 1( )l l l . If the length of frame

is h, the mutual inductance between the conductor and frame is

3



(1) 01 2ln( / )

2

hl l

(2) 0

2 1ln( / )2

l lh

(3) 02 1( / )

2

hl l

(4) 0

1 2( / )2

l lh

8. The electric field of an electromagnetic wave

0ˆ( , ) 2 cos( )E r t E z x y t

If ‘c’ stands for the velocity of the wave, the magnetic field ( , )B r t is

(1) 0

1ˆ ˆ( , ) ( ) cos( )

2B r t x y E x y t

c

(2) 0

1ˆ ˆ( , ) ( ) cos( )B r t x y E x y t

c

(3) 0

1ˆ ˆ( , ) ( ) cos( )B r t x y E x y t

c

(4) 0

1ˆ ˆ( , ) ( ) cos( )

2B r t x y E x y t

c

9. A metallic ring of area 21cm and resistance 10 is placed in a perpendicular time-varying magnetic

field which has the following form

0.5( ) 2 cos(2 )tB t e t

Where B is in Tesla and t is in seconds. The net charge that flows past any point in the ring from

0t to t is

(1) 1 c (2) 3 c (3) 5 c (4) 20 c

10. The refractive index of a medium in which the electric field of an electromagnetic wave is given in

m.k.s units by 7 7 15

0ˆcos(10 10 10 )E E x y t z is

(1) 1.4 (2) 3.0 (3) 4.2 (4) 6.0

11. The electric field of a plane electromagnetic wave propagating in free space is described by

0ˆsin( )E E kx t y . The time average pointing vector for the wave

(1) 2

0

22

E

c (2)

2

0

02

E

c (3)

2

0

2

02

E

c (4)

2

0

0

3

2

E

c

12. The electric field ( , )E r t at a point r at time t in a metal due to the passing of electrons can be

described by the equation

2

2 2

2 2

1 ( , )( , ) ' ( , )

E r tE r t E r t

c t

Where is a characteristic associated with the metal and c is the speed of light in vaccum. The

dispersion relation corresponding to the plane wave solutions of the form exp ( )i k r t

is given

by

(1) 2 2 2 2'c k (2) 2 2 2 2'c k

(3) 'ck (4) 'ck

13. An electron with kinetic energy of 10keV is moving in a circular orbit in a plane perpendicular to a

uniform magnetic field of strength 2 tesla 4( 2 10 )gauss . The period of rotation is nearest to

(1) 122.8 10 s (2)

125.6 10 s

(3) 111.8 10 s (4)

101.1 10 s

4



14. A loop of radius r carries a uniformly distributed charge. Assuming the potential at infinitely to be

zero, the ratio of the potential at a height 2r on the axis to that at a height 3r is

(1) 1

2 (2) 2 (3)

1

2 (4) 2

15. Two identical point charges of mass m and charge q are separated by a distance d and are moving at

a relative speed u . What is their relative speed when they are at a large distance from each other.

(1) 2

2

0

Qu

md

(2)

22

0

2Qu

md

(3) 2

2

0

Qu

md

(4)

22

0

2Qu

m md

16. The Poisson’s equation in CGS Gaussian system is

(1) 2

0

V

(2) 2 4V

(3) 2 4V (4) 2 0V

17. For a plane electromagnetic wave given by

cos cos ;zE a x ct

sin sinyH a x ct

The instaneous value of pointing vector will be

(1) 2 sin 2 sin 2a x ct (2) 21sin 2 sin 2

4a x ct

(3) 2 sin 2 sin 2a x ct (4) 21sin 2 sin 2

4a x ct

18. Larmar formula for the power radiated by a non-relativistically accelerated charged particle is given

by

(1) 2 2

3

0

1 2

4 3

e a

c (2)

2 2

3

2

3

e a

c

(3) 2

2

0

1 2

4 3

e a

c (4)

2 2

2

0

1 2

4 3

e a

c

19. If the electric field is ˆr

kE a

r

in cylindrical coordinates, the work needed to move a point charge

Q to a point at twice the radial distance is

(1) ln 2kQ (2) kQ (3) ln 2kQ (4) kQ

20. The radius R of a loop carrying a current I is doubled, 2R R while the current is halved 2I I .

The magnetic moment M of the current loop is then

(1) M (2) 2M (3) M/2 (4) 4M

21. The sinusoidally time varying vector field

Is

(1) elliptically polarized (2) circularly polarized

(3) linearly polarized (4) unpolarized

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22. A plane electromagnetic wave travelling in vacuum is incident normally on a non-magnetic, non-

absorbing medium of refractive index n . The incident ( )iE reflected ( )rE and transmitted tE

electric fields are given as

0

0

0

exp

exp ;

exp

i i i

r r r

t t t

E E i k z t

E E i k z t

E E i k z t

If 0 2 /iE V m and 1.5n then the application of appropriate boundary conditions leads to

(1) 0 0

3 7/ , /

5 5r tE V m E V m (2)

0 0

1 9/ , /

5 5r tE V m E V m

(3) 0 0

2 8/ , /

5 5r tE V m E V m (4)

0 0

4 6/ , /

5 5r tE V m E V m

23. Consider the rectangular cavity as shown in figure. If a b c , then the dominant mode is

(1) 011TE (2) 110TM (3) 101TE (4) 101TM

24. A magnetic field 0ˆ ˆ ˆ( 2 4 )B B i j k exist at a point. If a test charge moving with a velocity

0ˆ ˆ ˆ(3 2 )v i j k experiences no force at a certain point, the electric field at that point in SI units is

(1) 0 0ˆ ˆ ˆ(3 2 4 )E v B i j k (2) 0 0

ˆ ˆ ˆ( 4 )E v B i j k

(3) 0 0ˆ ˆ(14 7 )E v B j k (4) 0 0

ˆ ˆ(14 7 )E v B j k

25. A circular conducting ring of radius R rotates with constant angular velocity about its diameter

placed along the x -axis. A uniform magnetic field B is applied along y -axis. If at time 0t the

ring is entirely in xy -plane. The e.m.f induced in the ring at time 0t is

(1) 2 2B R t (2) 2 tan( )B R t

(3) 2 sin( )B R t (4) 2 cos( )B R t

26. A parallel-plate guide operates in the TEM mode only over the frequency range 0 3f GHz . The

dielectric between the plates in Teflon 2.1r . The maximum allowable plate separation b is

(1) 3.4 cm (2) 6.8 cm (3) 4.3 cm (4) 8.6 cm

27. A magnetic field B is ˆBz in the region 0x and 0 elsewhere. A rectangular loop, in the xy-plane, of

side l (along the x-direction) and h (along the y-direction) is inserted into the 0x region from the

0x region at a constant velocity ˆv vx . Which of the following value l and h will generated the

largest E.M.F.

(1) 8, 3l h (2) 4, 6l h (3) 6, 4l h (4) 10, 12l b

6



28. Two parallel plate capacitors separated by distance x and 1.1x respectively, have a dielectric

material of dielectric constant 3.0 inserted between the plates, and are connected to a battery of

voltage v. The difference in the charge on the second capacitor compared to the first is

(1) 66% (2) 20% (3) -33% (4) -10%

29. Radio wave of the wave length 360 m are transmitted from a transmitter, the inductance of a coil

which must be connected with a capacitor of capacity 1.2 f in a resonant circuit to receive these

wave will be approximately

(1) 103H (2) 10

2H (3) 10

-4H (4) 10

-8H

30. The area of circular coil with 2000 times is 10cm2. Its plane perpendicular to a magnetic field of

20.3

wb

m, is rotated by o180 . The change in magnetic flux is

(1) 1.2wb (2) 1.2wb (3) 0.6wb (4) 0.6wb

31. The entropy of a gas containing N particles enclosed in a volume V is given by

3/2

5/2lnB

aVeS Nk

N

where E is the total energy, a is a constant and Bk is the Boltzmann constant. The chemical potential

is of the system at a temperature T is given by

(1) 3/2

5/2

5ln

2B

aVEk T

N

(2)

3/2

5/2

3ln

2B

aVEk T

N

(3) 3/2

5/2

5ln

2B

aVEk T

N

(4)

3/2

5/2

5ln

2B

aVEk T

N

32. Let v , vx y and v z denote the components of the velocity along x y and z directions, respectively, of

an ideal gas particle. At absolute temperature T, the average value of the product 2 2 2v v vx y z is

proportional to

(1) 1/2T (2) T (3) 3/2T (4) 3T

33. The intensity of radiation emitted by the sun has its maximum value at a wave length of 500nm. The

corresponding value for the state Polaris is 380 nm. Assuming that these stars behave like black

bodies the ratio (TS/TP) of the surface temperature of the sun and Polaris is.

(1) 1.70 (2) 1.32 (3) 0.76 (4) 0.58

34. What is the maximum amount of work that can be extracted from an object of heat capacity Cp,

initially at a temperature T2, by a heat engine that operates between this object and a reservoir at

temperature T1?

(1) CP(T2-T1) (2) CP(T2-T1) - CP T1ln (T2/T1)

(3) CP(T2-T1)ln (T2/T1) (4) 2 1

P

T TC

2

35. A system having N non-degenerate energy eigen states is populated by N identical spin-zero particles

and 2N identical spin-half particles. There are no interactions between any of these particles. If

N=1000, the entropy of system is closet to

(1) 13.82 KB (2) 0 (3) 693.1 KB (4) 1000 KB

7



36. A car tyre is slowly pumped up to a pressure of 2 atmospheres in an environment at o15 C , at this

point, it bursts. Assuming the sudden expansion of the air (a mixture of O2 and N2) that was inside

the tyre to be adiabatic its temperature after the burst is

(1) o55 C (2) o37 C (3) o26 C (4) o9 C

37. A collection of N two-level system with energies O and E > O is in the thermal equilibrium at

temperature T. for T . The specific heat approaches

(1) 0 (2) BNK (3) 3

2BNK (4)

38. An ideal gas expand in a process in which its pressure depends on the volume as v

0P P e . Where

0P and are two positive constants. In n is the number of moles in the gas, the maximum

temperature that it will attain in this process is (R is the universal gas constant)

(1) 0 /P e nR (2) 3

0 /P n R (3) 0 /eP nR (4) 2

0 /P nR

39. The probability of a system to be in a state with energy E at temperature T is proportional to /E Kte . If

the system in question is a one dimensional quantum harmonic oscillator of frequency ω , the

average energy at temperature T is

(1) 2

(2)

/ 1

2BK Te

(3) /

1 1

1 2BK Te

(4) /

1 1

1 2BKe

40. The peaks of emission measured from two different black bodies 1 and 2 are found to be at the

frequencies 1v and 2v respectively, with 1 22v v . The temperature of body 1 is known to be 1T , then

the temperature 2T of body 2 is

(1) 1

2

T (2) 1T (3) 12T (4) 12T

41. A Carnot engine named A operates between temperatures 1T and 2 1 2T T T . A second Carnot engine

named B uses all the heat rejected by the engine A as input and operates between temperature 2T and

3 2 3T T T . The efficiency of this coupled engine system is

(1) 2

1

1T

T (2) 3

2

1T

T (3) 3

1

1T

T (4) 32

1 2

1 1TT

T T

42. A vessel containing equal number of molecules of two monatomic gases. A and B is at temperature

T. their masses are m and 4m respectively. The root mean square velocity of the atoms in the mixture

is

(1) 3 8

4

kT

m (2)

8kT

m (3)

3 16

4 5

kT

m (4)

16

5

kT

m

43. Consider a system of N sites with one spin per site each spin can assume only one of two values,

namely +1 or 1. The number of states with N, spins with the value +1 and N spins with the value 1

is (note N N N )

(1) N N

N N

(2) ! !

!

N N

N

(3) ! !

! !

N N

N N

(4) !

! !

N

N N

8



44. A system of N non-interacting classical particles each of mass m, is in a 2D. Harmonic potential of

the form 2 2( ) ( )V r x y where ve constant. The Canonical partition function of the system

at temperature T is 1/ BK T

(1)

2

2

N

m

(2)

2

2N

m

(3) 2

N

m

(4) 2

2

2N

m

45. The partition function of 1D H.O is/2

1

eZ

e

, where

1

K T . Then the average number of

oscillators is

(1) 1

1e (2)

1

1 e (3)

1

1 e (4)

1

1 e

46. A collection N of non-interacting spins

, 1, 2,..... , 1i iS i N S is kept in external magnetic field B at a temperature T. The Hamiltonian of

the system isi

iH B S .What should be the minimum value of

B

B

k T

for which the mean value

1

3iS ?

(1) 1

ln 22

N (2) 2ln 2 (3) 1

ln 22

(4) ln 2N

47. A classical particle of mass m with position x and momentum p is moving in one-dimension

harmonic oscillator potential 2 21v( )=

2x m x . It is in contact with a heat bath at temperature T. which

of the following is true.

(1) 2 0BK Txp x

(2)

20 BK T

xp xm

(3) B BK T K Txp x

m (4) 2

20 BK T

xp xm

48. A sample of ideal gas with initial pressure p and v is taken through isothermal expansion during

which the change in s is found to be s the universal gas constant is R then the work done by the gas

is given by

(1) v

p s

nR

(2)

vp

n sR (3)

vp s

nR

(4)

vp

nRs

49. An ensemble of N three level system with energies 0 0,0,E is in thermal equilibrium at temp

T. The free energy of the system at high temperature (i.e. 0 1) is

(1)

2

0ln 2

2B

BNK T

(2) ln 2NKT

(3) ln3NKT (4)

2

0ln 3

3BNK T

9



50. A system has energy level 0 0 0, 2 ,3 ....E E E where the excited levels are triply degenerate four non

interacting Boson are placed in the system. If the total energy of these boson is 05E . The number of

microstates is

(1) 2 (2) 3 (3) 4 (4) 5

51. If the volume of a three dimensional free fermi gas is decreased by a factor of 8 at zero temperature.

Its internal energy changes by a factor

(1) 8 (2) 2 (3) 4 (4) 1/8

Date: 26/Nov/16, M.M:200 Timing: 2:00 H

BOOKLET CODE SUBJECT CODE

PHYSICAL SCIENCE TEST SERIES # 2 Thermal, Statistics & Electromagnetic Theory

ANSWER KEY

1.(4) 2.(1) 3.(2) 4.(4) 5.(3) 6.(3) 7.(3) 8.(3) 9.(4) 10.(3)

11.(2) 12.(1) 13.(3) 14.(4) 15.(3) 16.(1) 17.(4) 18.(1) 19.(1) 20.(2)

21.(1) 22.(3) 23.(1) 24.(4) 25.(3) 26.(1) 27.(4) 28.(4) 29.(4) 30.(2)

31.(3) 32.(4) 33.(3) 34.(2) 35.(3) 36.(2) 37.(1) 38.(1) 39.(3) 40.(1)

41.(3) 42.(1) 43.(4) 44.(4) 45.(1) 46.(4) 47.(4) 48.(3) 49.(3) 50.(2)

51.(3)

UGC POINT ACADEMY LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM

05 A

Documents

LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM 2016/PHYSICS/2.pdfthe line passing through the centre and parallel to the length of two parallel plates with a spacing of 0.1 m. The plates