A

1. A conducting sphere of radius 0.05 meter has a charge of 1.0 x 10 -9 C deposited on it. The magnitude of the electric field in N/C inside the sphere at a distance of 0.25 m from the cnetr of the sphere is

A. 0B. 450C. 900D. 4500E. 90,000

2. A circular wire loop of radius R rotates with an angular frequency ω in a uniform magnetic field B. If the induced emf produced in the loop is A sin(ωt), the angular frequency ω of the loop would be equal to

A. πA R2

B

B. π BR2

A

C.2πRBA

D.A

π R2B

E.ABπ R2

3. A line charge carries a uniform charge density λ. The electric field at a distance r from the wire would be proportional to

A.λ

2π r2

B.λ

2π r❑

C. a function of all r, θ and φ

A

D. λ2

2π r2

E. λ2

2π r❑

4. Let z=x+iy. Then the imaginary part of 1/z, Im(1/z) would be:

a. –y/(x2+y2)b. +y/(x2+y2)c. –x/(x2+y2)d. +x/(x2+y2)e. (x+y) /(x2+y2)

5. Which of the following series corresponds to cos2 z:

a. 1− z2

2 !+ z4

4 !−⋯⋯⋯

b. 1+ z2

2!+ z4

4 !+⋯⋯⋯

c. 1−4 z2

2 !+16 z4

4 !−⋯⋯⋯

d. 1−2 z2

2!+ 4 z4

4 !−⋯⋯⋯

e. 1+ 2 z2

2 !+ 4 z4

4 !+⋯⋯⋯

6. Which of the following results is correct if we take the divergence of the function

V= y2 i+(2x2 y+z3 ) j−2 y z3 ka. 2y+ 2x2-6yz2

b. 4xy+3z2-6z3

c. 0d. 2y+4xy+2x2+3z2-6yz2

A

e. 2x2-6yz2

7. If z is a complex number the roots of z3-8 =0 areA. 2, 2, and -2

B. 2, 1+ i2 and

1−i2

C. 2, −1+i √3 and −1−i √3

D. 2, 1+√3 i2

and 1−√3 i2

E. none of the above

8. From the solution of the differential equation x=−k2 x , for the boundary conditions x (0 )= xo and x (0 )=0, the velocity x (t )=

A. xo sinkt

B. xo (sin(kt) + cos(kt))

C. xo exp-ikt

D. xo cos(kt)

E. xo e−ktcos(kt)

A

9. The speed of a relativistic particle having a momentum 5MeV/c and a total relativistic energy of 10Mev is

A: cB: 0.75 c

C: c√3

D:c2

E.c4

10. If the absolute temperature of a black body is increased by a factor of 4 the energy radiated per second per unit area

A. decreases by a factor of 256.B. `decreases by a factor of 16.C. increases by a factor of 16D. increases by a factor of 64E. increases by a factor of 256

11. The speed of a wave traveling through a stretched string is directly proportional to the A. density per unit length of the stringB. square of the tensionC. square root of the tensionD. square of the density per unit length

A

E. square root of the density per unit length

12. A ray of light in a dense liquid, index of refraction = 1.4, approaches the boundary surface between the liquid and air at angle of incidence whose sine = 0.8. On the basis of this data, the following statement is correct:

A. it is impossible to predict the behavior of the light ray on the basis of the information supplied

B. the ray will be internally reflectedC. the sine of the angle of refraction of the emergent ray will be less than 0.8D. the sine of the angle of refraction of the emergent ray will be greater than 0.8E. the ray will be totally absorbed

13. A luminous object is separated from a screen by a distance D. What is the greatest focal length a lens could have and still focus the object on the screen?

A. 4DB. 2DC. DD. ½ DE. (1/4)D

A

14. The de Broglie wavelength of the matter wave associated with an electron of mass m accelerated by a voltage V is, (h: Planck’s constant)

A. h

√2emV

B. h

2emV

C. (h2 e2V 2/m2)

D. √ h2 emV

E. 2emVh

15. Light is composed of quanta, as is demonstrated by the photoelectric effect. It is found that the photoelectric current depends on

A. the color of the incident lightB. the frequency of the incident lightC. the phase and frequency of the incident lightD. the intensity and the frequency of incident E. the intensity of the incident light

A

16. In the Bohr model the electron emits radiation when it drops from a higher n to a lower n level. Using this model we find that the ratio of the emitted frequencies as the electron drops from the n=3 to the n=1 level over that emitted when it drops from the n=3 to the n=2 levels is

A. ν31

ν32=9

4

B.ν31

ν32=36

5

C.ν31

ν32=16

5

D.ν31

ν32=32

5

E.ν31

ν32= 5

36

17. A ring of radius R lying in the xy plane carries a uniform charge density λ. At a point a on the axis of the ring (z=a), the electric field

A: has both x and y components that are equal in magnitude

B: has both x and y components that are not equal in magnitude

C: has only a z component

D: has x,y,z components all of unequal magnitudes.

E: is zero

A

18. The potential energy of a body of mass m constrained to move on a straight line is U=kx4

where k is a constant. At a position xo the force on the body is

A. F= 4mk xo3

B. F= - 4kmxo

3

C. F= - 4k xo3

D. F= - 4k (x−xo )3

E. F=- 4k (x−xo )2

19. Two spherical bodies of masses M and 4M are placed a distance d apart. The net gravitational force due to the two masses is found to be zero at a distance R from the larger mass, along the line joining the centre of the two masses. The value of R is

A. d/3B. 2d/3

A

C. d−d √3

D.2d3

E. d/5

A

20. The equation of motion of a rocket in free space can be written as m dvdt

+u dmdt

=0, where u is a

constant. Given that at t=0 , v=0 and m=mo, the equation can be solved for the velocity v to yield,

A: v= u mo

m

B: v= u expm o

m

C: v= u exp−mo

m

D: v= u ln( mmo )E: v=u ln(mo

m )

21. A particle of mass m undergoes harmonic oscillation with amplitude A and period To. A force proportional to the speed of the particle F=-kv is now introduced. The particle continues to oscillate but with

A: same amplitude but increased time period.B: increased amplitude but decreased time period.C: decreased amplitude and decreased time period.D: decreased amplitude and increased time period.E: decreased amplitude but same time period

22. A disc of moment of inertia I1 is rotating with angular frequency ω.A second disc of moent of inertia 2 I1 drops onto the first disc and they begin to rotate together. The new frequency of rotation would be

A. The same as before.

B. ω3

C. zero (there would be no rotation).D. 3ω

E.ω2

A

23. A block of mass m slides down an inclined plane at constant speed. The plane has a height h and length L and is inclined at an angleθ to the horizontal. The coefficient of kinetic friction is μ . As the mass slides all the way down the plane till it reaches the ground, the energy dissipated due to friction is

A. mghB. μmghcosθC. mgLD. μmgLE. mgh sinθ

24. Light of frequency ν and wavelength λ passes from air (n=1) to a medium of refractive index 2. In the given medium the following conditions would be correct

A. Both the frequency and wavelength are decreased by a factor of twoB. The frequency remains unchanged while the wavelength is decreased by a factor of two.C. The frequency is decreased by a factor of two while the wavelength is unchanged.D. The speed of the wave its frequency are both decreased.E. The speed of the wave and its wavelength are both decreased

25. Two small charged objects repel each other with a force F when separated by a distance d. If the charge on each object is reduced to one-fourth of its original value and the distance between them is reduced to d/2 the force becomes:

A. F/16B. F/8C. F/4D. F/2E. F

A