ANDHERI / BORIVALI / DADAR / CHEMBUR / THANE / NERUL / KHARGHAR / POWAI

MT – 4 – Physics

1. A body is falling freely under the action of gravity alone in vacuum. Which of the following

quantities remain constant during the fall:

(1) Kinetic energy (2) Potential energy

(3) Total mechanical energy (4) Total linear momentum

2. A liquid rises in a vertical tube. The relation between the weight of the liquid in the tube, surface

tension of the liquid T and radius of the tube r is given by, if the angle of contact is zero

(1) 2W r T (2) W 2 rT (3)

2W 2r T (4) 33

W r T4

3. A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the

circumference of the discs coincide. The centre of mass of the new disc is R from the centre of the

bigger disc. The value of is

(1) 1

3 (2)

1

2 (3)

1

6 (4)

1

4

4. Three identical blocks A,B and C, each of mass 2kg are kept on a smooth horizontal surface. Block

A is given a horizontal velocity 10m/s towards B (as shown in figure). Block B and C are attached

with a spring. Find change in velocity of centre of mass of system A+ B+ C if A collides with B

elastically.

(1) 5 m/s (2) 10 m/s (3) 20 m/s (4) zero

5. A force of 100N is applied on a block of mass 3kg as shown in the figure. The coefficient of friction

between the surface and the block is 1

.3

The frictional force acting on the block is?

(1) 15N downwards (2) 25N upwards (3) 20N downwards (4) 30N upwards

6. Force of attraction between two point electric charges placed at a distance d in a medium is F. What

distance apart should these be kept in the same medium, so that force between them becomes F/3?

(1) 2 3 d (b) 3d (3) 9d (4) 3 d

7. An arc of radius R is shown in the diagram with linear charge density. Find electric field at the centre

(1) k

4 2R

(2)

k2

R

(3)

k

R

(4) zero

8. Two particles each of mass M is attached to the two ends of a massless rigid non-conducting rod of

length L. The two particles carry charges +q and -q respectively. This arrangement is held in a region

of uniform electric field E such that the rod makes a small angle 0( 5 ) with the field direction. The

time period of rod is (rod oscillates about its centre of mass)

(1) ML

22qE

(2) ML

2qE (3)

ML

2 2qE

(4)

ML4

2qE

9. Two particles of masses m and 2m with charges 2q and 2q placed in a uniform electric field E and

allowed to move for the same time. The ratio of their kinetic energies will be

(1) 2 : 1 (2) 8 : 1 (3) 4 : 1 (4) 1 : 4

10. Consider a conducting spherical shell of radius R with its centre at the origin, carrying uniform

positive surface charge density. The variation of the magnitude of the electric field E (r) and the

electric potential V(r) with the distance r from the centre, is best represented by the graph (Here

dotted line represents potential curve and bold line represents electric field curve)

(1) (2)

(3) (4)

11. A small ball is pushed from a height h along a smooth hemispherical bowl. With what speed should

the ball be pushed so that it just reaches the top of opposite end of bowl? The height of the top of the

bowl is R.

(1) 2gh (2) 2gR (3) 2g(R h) (4) 2gR(R h)

12. A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path(s)

shown in figure as

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

13. Figure shows a disc of mass M and radius R lying in the xy-plane with its centre on x-axis, at a

distance a from the origin. The moment of inertia of the disc about x-axis will be

(1) 21MR

2 (2) 21

MR4

(3) 2 21M(R 2a )

2 (4) 2 21

M(R 4a )4

14. A child is standing with folded hands at the center of a platform rotating about its central axis. The

kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of

the system doubles. The kinetic energy of the system now is

(1) 2K (2) K/2 (3) K/4 (4) 4K

15. A biconvex lens has a focal length f, It is cut into two parts along a line perpendicular to principle

axis. The focal length of each part will be

(1) f/2 (2) f (3) (3/2)f (4) 2f

16. In a plano-convex lens the radius of curvature of the convex lens is 10 cm. If the plane side is

polished, then the focal length will be (Refractive index = 1.5)

(1) 20.5 cm (2) 10 cm (3) 15.5 cm (4) 5 cm

17. The refractive index of a prism for a monochromatic wave is 2 and its refracting angle is 060 . For

minimum deviation, the angle of incidence will be

(1) 030 (2) 045 (3) 060 (4) 075

18. The direction of ray of light incident on a concave mirror is shown by PQ while directions in which

the ray would travel after reflection is shown by four rays marked 1, 2, 3 and 4 (figure). Which of the

four rays correctly shows the direction of reflected ray?

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

19. An object weight 72N on earth. Its weight at a height of R/2 from earth is

(1) 32N (2) 56N (3) 72N (4) zero

20. The satellite of mass m revolving in a circular orbit of radius r around the earth has kinetic energy E.

Then its angular momentum will be

(1) 2

E

mr (2)

2

E

2mr (3) 22Emr (4) 2Emr

21. The escape velocity of a body projected from the surface of the earth vertically upwards is 11.2 km/s.

If the body is projected in a direction making an angle 030 with the vertical, then the new escape

velocity will be

(1) 11.2

km / s2

(2) 3

11.2 km / s2

(3) 22.4 km/s (4) 11.2 km/s

22. A satellite moves around the earth in a circular orbit of radius R with speed v. If the mass of the

satellite is M, its total energy is

(1) 21

Mv2

(2) 21

Mv2

(3) 23

Mv2

(4) 2Mv

23. The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite

is increased to four times the previous value, the new time period will become

(1) 20 hours (2) 10 hours (3) 80 hours (4) 40 hours

24. 1 gm of ice is passed into a container having 2gm water at 035 C . The equilibrium temperature of the

mixture is

(1) 00 C (2) 012 C (3) 010 C (4) 035 C

25. The temperature of an ideal gas is increased from 120K is 480 K. If at 120 K, the root mean square

velocity of the gas molecules is v, then at 480 K, it will be

(1) 4v (2) 2v (3) v

2 (4)

v

4

26. The P-V diagram of process on a system is shown in figure. During the process, the work done by

the system

(1) increases continuously

(2) decreases continuously

(3) first increases, becomes maximum and then decreases

(4) first decreases, becomes minimum and then increases

27. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its

absolute temperature. The ratio p vC / C for the gas is

(1) 3

2 (2)

4

3 (3) 2 (4)

5

3

28. A particle executing simple harmonic motion along y -axis has its motion described by the equation

y Asin( t) B. The amplitude of the simple harmonic motion is

(1) A (2) B (3) A + B (4) A B

29. If a simple pendulum oscillates with an amplitude of 50 mm and time period of 2 sec, then its

maximum velocity is

(1) 0.10 m/s (2) 0.16 m/s (3) 0.8 m/s (4) 0.26 m/s

30. A man measured the period of a simple pendulum inside a stationary lift and finds it to be T s. If the

lift accelerates upwards with an acceleration g/4, then the period of the pendulum will be

(1) T (2) T

4 (3)

2T

5 (4) 2T 5

31. Four massless springs whose force constants are 2k, 2k, k and 2k respectively are attached to a mass

M kept on a frictionless plane (as shown in figure). If the mass M is displaced in the horizontal

direction, then the frequency of the system

(1) 1 k

2 4M (2)

1 4k

2 M (3)

1 k

2 7M (4)

1 7k

2 M

32. A particle moves such that its acceleration a is given by a = -bx, where x is the displacement from

equilibrium position and b is a constant. The period of oscillation is

(1) 2 b (2) 2

b

(3)

2

b

(4) 2

b

33. A wire of length L and cross-sectional area ‘A’ is made of a material of Young’s modulus Y. If the

wire is stretched the amount x, then work done is

(1) 2YAx

2L (2)

2YAx

L (3)

YAx

2L (4)

2YAx L

34. What will be the height of liquid column in the capillary on the surface of moon if it is h on surface

of earth

(1) h (2) h/6

(3) 6h (4) information is sufficient

35. The liquid meniscus in capillary tube will be convex upwards, if the angle of contact is

(1) Greater than 090 (2) Less than 090

(3) Equal to 090 (4) Equal to 00

36. An incompressible liquid flows through a horizontal tube shown in the following fig. Then the

velocity v of the fluid is

(1) 3.0 m/s (2) 1.5 m/s (3) 1.0 m/s (4) 2.25 m/s

37. Figure shown below is a distribution of charges. The flux of electric field due to these charges

through the surface S is

(1) 03q / (2) 02q / (3) 0q / (4) zero

38. If AB

| A B | ,2

then angle between A and B is

(1) 00 (2) 030 (3) 045 (4) 060

39. A car accelerates from rest at a constant rate of 22m/s for some time. Then, it retards at a constant

rate of 24m/s and comes to rest. What is the maximum speed attained by the car, if it remains in

motion for 3 seconds?

(1) 2 m/s (2) 3 m/s (3) 4 m/s (4) 6 m/s

40. A food packet is dropped from a helicopter rising up with a velocity of 14ms . The magnitude of

velocity of the packet after three seconds will be

(1) 120.4ms (2)

125.4ms (3) 128.4ms (4)

130.4ms

41. The spatial distribution of the electric field due to charges (A, B) is shown in figure. Which one of

the following statements is correct?

(1) A is +ve and B -ve and |A| > |B|

(2) A is -ve and B +ve; |A| = |B|

(3) Both are +ve but A > B

(4) Both are -ve but A > B

42. The value of electric potential at any point due to any electric dipole is

(1) 2

p rk

r

(2) 3

p rk

r

(3) 2

p . rk

r

(4) 3

p . rk

r

43. An object of mass 3m at rest splits into three equal fragments. Two fragments have velocities

ˆ ˆv j and vi . The velocity of the third fragment is

(1) ˆ ˆv( j i) (2) ˆ ˆv(i j) (3) ˆ ˆv(i j) (4) ˆ ˆv(i j)

2

44. A ball A, moving with kinetic energy K, makes a head on elastic collision with a stationary ball with

mass n times that of A. The maximum potential energy stored in the system during the collision is

(1) K/n (2) (n 1)K

n

(3)

(n 1)K

n

(4)

nK

(n 1)

45. A particle executing SHM has a maximum speed of 30 cm s-1 and a maximum acceleration of 60 cm

s-2. The period of oscillation is

(1) s (2) s2

(3) 2 s (4) s

t

ANDHERI / BORIVALI / DADAR / CHEMBUR / THANE / NERUL / KHARGHAR / POWAI

MT – 4 – Physics - (ANSWER KEY)

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

6. (4) 7. (4) 8. (1) 9. (1) 10. (4)

11. (3) 12. (4) 13. (2) 14. (2) 15. (4)

16. (2) 17. (2) 18. (2) 19. (1) 20. (3)

21. (4) 22. (1) 23. (4) 24. (1) 25. (2)

26. (1) 27. (1) 28. (1) 29. (2) 30. (3)

31. (2) 32. (2) 33. (1) 34. (3) 35. (1)

36. (3) 37. (2) 38. (2) 39. (3) 40. (2)

41. (1) 42. (4) 43. (3) 44. (4) 45. (1)

ANDHERI / BORIVALI / DADAR / CHEMBUR / THANE / NERUL / KHARGHAR / POWAI

MT – 4 – Physics

(SOLUTION)

1. As gravitational force is conservative so total mechanical energy will remain conserve.

2.

3.

4. No external force or impulse so no change in velocity of centre of mass of system A + B + C

5.

30 + fr = 50

Fr = 20N downward

6.

7.

8.

9. qE

v .tm

2 2 2 2 2 2

2

2

1 1 q E t 1 q E tKE = mv m

2 2 m 2 m

2q

KEm

22

1 1 2

2

2 2 1

(KE) q m 2q 2m 2

(KE) q m 2q m 1

10.

11.

12.

13.

14.

15. The focal length of each part will be 2f.

16. Focal length, R

F2( 1)

10

F 10cm2(15 1)

17. Refractive index

sin i

sin A / 2

0

0

sin i2 or 2 sin 30 sin i

sin (60 / 2)

Or 012 sin i i 45

2

18. The PQ ray of light passes through focus F and incident on the concave mirror, after reflection the

ray, should become parallel to the principal axis and shown by ray-2 in the figure.

19. W = 72 = mg

20. 21E mv v 2E / m

2

And 2

22mv 2ErL mvr r 2Emr

2v 2E / m

21. Escape speed does not depend on angle of projection.

22. 21K Mv

2

Total energy 21K Mv

2

23.

24. The amount of heat available in water = 2 1 (35 0) 70 cal. The heat needed to melt the ice

completely is 1 80 80 cal. So ice will not melt completely and temperature of water falls to 00 C.

25.

Or 2 1v 2v

26. During the process, W P V; V increasing, so work done increases.

27. 3P KT and

PV

PV nRT TnR

So

3PV

P knR

Or 3/2PV constant

3 / 2

28. In y = Asin t B, the oscillating part is Asin t so amplitude of motion is A.

29.

30.

31. The equivalent system is shown in figure

The equivalent force constant of which

32. a = -bx, on comparing with

2a x

We get b

2 2

Tb

33.

34. As 2T

hR g

2T

h 6hR g / 6

35. For the convex meniscus, the angle of contact should be greater than 090 .

36. 1 1 2 2Av A v A v

Or A 3 A 1.5 1.5A v

v = 1 m/s

37.

38.

39.

40.

41. Spacing between the lines of field increases from A to B, and so magnitude of charge at B will be

less than A.

42.

43.

44.

45.