MULTIPLE CHOICE QUESTIONS (SINGLE OPTIONS CORRECT)

1. A block of mass m is resting on the rough horizontal ground. Minimum force required to move it

is 3

5

mg. Then coefficient of friction is

(a) 1

5(b)

4

5

(c)

1

4

(d)

3

4

2. A nucleus whose decay constant is

is produced at a constant rate of P nuclei per second. if N

is the no. of nuclei present after time t then

dN

dt

is

(a)

Pe t

(b) P

e t

1

1 c h (c)

P

te t

(d) none of the above

3. The effective resistance between A & B of the

shown network. Where resistance of each resis-

tor is R, is

(a) 8

11

R(b)

6

11

R

(c) 6

5

R(d) none of these

4. A potentiometer wire AB as shown is 40 cm long

of resistance 50 / m free end of an ideal volt-

meter is touching the potentiometer wire. What

should be the velocity of the jockey as a function

of time so that reading in voltmeter is varying with

time as (2sin

t

)

(a) 10

sin

tcm/s (b) 10

cos

tcm/s

(c) 20

sin

t cm/s (d) 20

cos

tcm/s

5. A resistor of resistance R, capacitor of capacitance C and inductor of inductance L are connected

in parallel to AC power source of voltage

0 sin t

. The maximum current through the resistance

is half of the maximum current through the power source. Then value of R is

(a)

3

1

C

L (b)

31

LC

(c) 51

CL (d) none of these

6. An real object of 2cm length is placed upright at a distance of x cm from a spherical mirror with its

base on the principle axis its image is formed at distance x + 20 cm. The image is real inverted &

4 cm in length. Find focal length of spherical mirror.

(a) 30 cm (b) 40/3 cm (c)40 cm (d) 30/4 cm

v A B

4v

10

10

AB

7. A sample of an ideal gas is taken through a cyclic process whose P-V graph is in the shape of the

rectangel consisting of isochoric and isobaric process. If maximum pressure of the gas is P0. The

value of minimum presure of the gas so that efficiency of cycle is 20% , is

(a) 0.2 P0

(b) 0.4 P0

(c) 0.8 P0

(d) data insufficient

8. One end of ideal string tied up with fixed support & other end is tied with a bob. The string is

released from horizontal position. When string makes an angle of with vertically downward

direction then the acceleration vector of bob is horizontal. Then

is

(a)tan -1(1) (b) tan-1(1/2) (c) tan-1

3d i

(d) none of these

9. A massless string of length l, cross-sectional area

A and Youngs modulus Y is tied up with a bob of

mass m. The bob is moving with constant angu-

lar speed in circular path of radius r as shown.

Find elongation

l

in the string assuming l

of radius r2(>r

1) containing water. A body of relative density 2 is placed on the top surface of ice

so that ice is just submerged. The increase in the water level is

(a)

9

10

1

2

2

2

1

2

l r

r r

FHG

IKJ

(b)

9

10

1

2

2

l r

r

FHG

IKJ

(c) l

10

1

2

2

2

1

2

r

r r

FHG

IKJ (d)

l

10

1

2

2

r

r

FHG

IKJ

14. A charged capacitor o fcapacitance C & having charge Q is to be

connected with another uncharged capacitor of capacitance C

as shown so that till the steady state is reached, find the value of

C if heat librated through the wires is maximum.

(a) zero (b) C (c) C/2

(d) 2C.

15. The electric field of a light wave at a point is E= (100 N/c) sin (3x 1015t)sin (6x 1015t) where t is

time in second. This light falls on a metal surface having work function of 2 eV, then maximum

possible kinetic energy of photoelectrons is about

(a)16 eV (b) 7 eV (c) 6 eV (d) 4 eV

16. Inclined plane AB & BC are at an inclination of 600 &300 from the horizontal respectively. Two

projectiles are thrown from A& C such that they strikes at B with same speed. The length AB is

1

3 m and length BC is 1m. If projectile from A is thrown with speed 2 m/s then the initial speed

of projectile thrown from C is

(a) 1/2 m/s (b) 1 m/s (c) 2 m/s (d) none of these

17. Three charges q, q and -2q are fixed on the vertices of an equilateral triangular plate of edge length

a. This plate is in equilibrium between two very large plates having surface charge density

1 2 and respectively. Find the period of small angular oscillation about an axis passing through

its centroid and perpendicular to plane. Moment of inertia of the system about this axis I.

(a) 20

1 2

I

q a (b) 2 2

0

1 2

I

qa

(c) 22

3

0

1 2

I

qa (d) 2

2 0

1 2

I

qa

18. A Particle is executing linear SHM. Its displacement from mean position, velocity & acceleration

at an instant are x, v and a respectively. Find amplitude of the motion.

(a) xv

a+

2

2(b)

xxv

a

22

(c)

x

v

axsin

2FHG

IKJ (d) none of these

19. A solid sphere of uniform density has radius equal to R. it has a cavity of radius R/2 such that the

centre of mass lies on the surface of the cavity. Find distance between centre of sphere and centre

of cavity.

(a) Zero (b) R/14 (c) R/6 (d) none of these

20. Find the moment of inertia of a semicircular ring of mass M and

radius R about an axis which is tangent to it and perpendicular to

the line joining its ends.

(a)

MR2

2

(b) MR2

(c)

3

2

2MR

(d) none of these

21. A container contains two immiscible liquids of density 1 and 2

( 2 1> ). A capillary of radius r is inserted in the liquid so that its

bottom reaches upto denser liquid and lighter liquid does not en-

ters in to the capillary. Denser liquid rises in capillary and atain

height equal to h which is also equal tocolumn length of lighter

liquid. Assuming zero contact angle find surface tension of heavier

liquid.

(a)

r gh22

(b)

2 2 r gh

(c) r

gh2

2 1 b g (d)

2 2 1 r ghb g

22. Three bodies A, B and C are situated at the vertices of an equilateral triangle ABC at t = 0. Each

of the particle moves with constant speed v. A always has its velocity along AB, B along BC a& C

along CA. During its journey A emit whistle of high frequency v0. Find frequency heard by B

considering speed of sund equal to c.

(a)

cv

c vv

+

F

HGGG

I

KJJJ

20(b)

c v

v vv

+

FHG

IKJ( / )2 0 (c)

c v

c vv

+

FHG

IKJ

( / )20 (d)

c v

c vv

+

FHG

IKJ/ 2 0

23. A particle of mass m is placed at a distance R from centre of a uniformly dense thin ring of mass m

and radius R on a n axis passig through its centre and perpendicular to its plane. Find the speed of

the particle when it reaches at the centre of the ring due to their mutual gravitation force.

(a) Gm

R

2 2 1d i(b)

Gm

R2

(c) Gm

R

2 1

2

d i(d) none of these

24. An infinitely long cylindrical radiation source is radiating with power of W watts per unit of its

length. The intensity of radiation, at a distance r from the axis of the cylinder is proportional to.

(a)

1

r

(b)

12r

(c)

1

r

(d) ln r

25. A point object is placed in air at a distance d from the pole of a

refracting convex surface on its principal axis & it starts moving

with speed v perpendicular to its principle axis as shown in figure.

Find the speed of its image if the radius of the convex surface is d.

(a) 0.5 v (b) 1.5 v (c) 2v

(d) 3v

---------------

h1

2

= 1 = 15.

O

26. An infinitely long current carrying wire carrying current i. A charge of mass m & charge q is

projected with speed v parallel to direction of current at a distance r from it. Then the radius of

curvature at point of projection is

(a)

2

0

rmv

q i

(b) 2

0

rmv

q i(c) r (d) cannot be determined

27. In a region at a distance r from z-axis magnetic field rB B rtk= 0

$ is present where B0 is constant t

is time. Then the magnitude of induced electric field at a distance r from z-axis is given by

(a) r

B2

0 (b) r

B2

02

(c)

r

B2

03

(d) none of these

28. A small square loop of edge length a and resistance R is moved with velocity v0 away from an

infinitely long current carrying conductor carrying current i so that the conductor and side of square

are always in same plane. Find induced current in loop at a separation of r.

(a)

0

2

2

ia v

r R

(b)

0

2

24

ia v

r R

(c)

0

2

22

ia v

r R

(d)

0

2

iav

rR

29. Current in a X-ray tube operating at 40 kV is 10 mA. 1% of the total kinetic energy of electrons

hitting the target is converted into X-rays. Then the heat produced in the target per second is

(a)396J (b) 4J (c) 400J (d) can not be determined

30. What is the minimum value of applied force F so

that both the block lifts up. Consider string to be

ideal and pulley to be massless & frictionless

(a) 4g (b) 8g

(c) 5g (d) 7g 123456789012345678901234567812345678901234567890123456781234567890123456789012345678

F

3kg 2kg