Tuesday, January 25, 2011

CPMT Sample Paper

1. A particle P is moving in a circle of radius a with a uniform
speed v. C is the centre of the circle and AB is the diameter.
The angular velocity of about A and C are in the ratio,
(a) 1 : 1 (b) 1 :2 (c) 2 :1 (d) 4 :2

2. A cube has numerically equal volume and surface area. The
volume of such a cube is
(a) 216 units (b) 1000 units (c) 2000 units (d) 3000 units

3. A person is standing on a turn table holding a pair of heavy
dumb bells, one in each hand with his arm outstretched. The
table is rotating with an angular velocity ω. The person
suddenly pushes the weight towards his chest. The angular
velocity of the turn table will
(a) become greater than ω
(b) become less than ω
(c) remain unchanged
(d) become 2ω if the masses of the dumb bells are equal

4. Two wires A and B of same material have their lengths in the
ratio 1:2 and their diameters in the ratio of 2:1. If they are
stretched with the same force, the ratio of the increase in
length of A to that of B will be
(a) 1:2 (b) 4:1 (c) 1:8 (d) 1:4

5. The speedometer of a car measures
(a) instantaneous speed
(b) average speed
(c) average acceleration
(d) instantaneous acceleration

6. A light body A and a heavy body B have equal linear
momentum. Then kinetic energy A is
(a) less than B
(b) equal to B
(c) zero
(d) greater than B

7. The released length of a spring is 0.3m and the spring constant
is 30N/m. If an external force F is used to stretch the spring
from 0.1 m to 0.2 m the work done by this force is
(a) 0.5 joule (b) 0.45 joule (c) 0.6 joule (d) 4.5 joule

8. In the given sets of unit which is not a unit of energy?
(a) Watt hour (b) Newton-meter (c) KG ms-1 (d) electron volt

9. On an application of a constant torque, a wheel initially at rest
is turned through an angle of 64 radian in 8 seconds. Its
angular acceleration is
(a) 2 rad/s2 (b) 3 rad/s2 (c) 1 rad/s2 (d) 4 rad/s2

10. The time period of satellite in a circular orbit of radius R is T.
The period of another satellite in a circular orbit of radius 4R is
(a) 4 T (b) T/4 (c) 8T (d) T/8

11. A body of mass 1kg initially at rest explodes and breaks into
three fragments of mass in the ratio 1:1:3. The two fragments
of equal masses fly off perpendicular to each other with a
velocity of 30 m/s. Velocity of heavier fragment is
(a) 24.1 ms-1 (b) 14.1 ms-1 (c) 141 ms-1 (d) 241 ms-1

12. A tank of volume 60 m3 is at a height of 40m above the
ground. If a pump of efficiency 60% can fill the tank in
15 minutes, the power consumed by the pump is
(a) 43.55 KW (b) 43.55 W (c) 4355 W (d) 435 KW

13. A hollow cylinder and a solid cylinder having the same mass and
same diameter are released from rest simultaneously from the
top of an inclined plane. Which will reach bottom first?
(a) the solid cylinder
(b) the hollow cylinder
(c) both will reach the bottom together
(d) the one having greater density

14. A box containing food supply is released from an airplane
moving horizontally at a height of 1600 ft with a velocity of
400 ft/sec. The box will move horizontally just before striking
against the earth through a distance
(a) 400 ft (b) 4000 ft (c) 6400 ft

15. A block of ice is floating in a liquid of specific gravity 1.2
contained in a beaker. When the ice melts completely, the level
of the liquid in the beaker
(a) will not change at all (b) will go down (c) will rise

16. The period of a satellite in a circular orbit near a planet is
independent of
(a) the mass of the planet (b) the radius of the planet
(c) the mass of the satellite (d) all the above

17. Of the basic forces existing nature, the most weak force is
(a) gravitational force
(b) electromagnetic force
(c) nuclear force
(d) weak force

18. A spring balance shows a reading 10 N when a stone of 0.5 kg
is suspended from it in a lift moving with a uniform acceleration.
The reading shown with same retardation is
(a) 10 N (b) 15 N (c) 0 (d) none of these

19. A metre stick is held vertically with one end on the floor and is
then allowed to fall. The speed of the other end when it hits
the floor assuming that the end at floor does not slip and
g=9.8 m/s2
(a) 3.2 m/s2 (b) 5.4 m/s2 (c) 7.6 m/s (d) 9.2 m/s

20. Two satellites A and B are orbiting around the earth in circular
orbits of the same radius. The mass of A is 16 times that of B.
The ratio of the period of revolution of B to that of A is
(a) 1:16 (b) 1:4 (c) 1:2 (d) 1:1

21. Two vectors of equal magnitude acting at a point have
resultant whose magnitude is equal to either of them. The
angle between the two vectors must be
(a) 00 (b) 1500 (c) 1200 (d) 600

22. A shell at rest explodes into two pieces of equal mass. The two
will be
(a) at rest
(b) move with different velocities in different directions
(c) same velocity in opposite directions
(d) same velocity in the same direction

23. The mass of a gas enclosed in a glass globe is increased from
M to 1.5M while the temperature remains constant. If the initial
pressure was 76 cm, calculate the final pressure.
(a) 114 cm (b) 50.66 cm (c) 22.8 cm (d) 19 cm

24. An inclined plane makes an angle of 300 with the horizontal. A
solid sphere rolling down the plane from rest without slipping
has a linear acceleration equal to
(a) g/3 (b) 2g/3 (c) 5g/7 (d) 5g/14

25. A river is flowing from west to east at a speed of 5 m/min. A
man on the south bank of the river capable of swimming at
10 m/min, in still water wants to swim across the river in the
shortest time. He should swim in the direction
(a) due north (b) 300 east of north
(c) 300 west of north (d) 600 east of north

26. A lorry and a car moving with the same kinetic energy are
brought to rest by the application of brakes, which provides
equal retarding forces. Then which of them will come to rest in
a short distance
(a) lorry (b) car
(c) both will cover same distance (d) data inadequate

27. A sphere of mass 4 kg strikes a spring whose force constant is
100 Nm-1 with a speed of 2 m/s. The kinetic energy of the
sphere when the spring is compressed by 0.1 m is
(a) 8 J (b) 7.5 J (c) 0.5 J (d) 8.5 J

28. Dimensions of power are
(a) [ML2T-3] (b) [M2LT-2] (c) [ML2T-1] (d) [MLT-2]

29. Which among the following is the largest when the time of
flight of a projectile is greatest?
(a) horizontal rage
(b) maximum height attained
(c) angle projectile with vertical
(d) both (a) and (b)

30. The dimensions of couple is
(a) [ML2T-2] (b) [MLT-2] (c) [ML1T-3] (d) [ML-2T-2]

31. When an explosive shell traveling in a parabolic path under the
gravity explodes. The centre of mass of the fragments will
continue to move
(a) along a hyperbolic path
(b) vertically upwards and then vertically downwards
(c) along the original parabolic path
(d) horizontally and then follows the parabolic path

32. The product of 0.0052 × 60000 expressed in scientific notation
(a) 3.12 × 102 (b) 3.12 × 10-2 (c) 3.12 × 104 (d) 3.12 × 10-5

33. A weight suspended from a spring oscillates up and down.
Acceleration of the weight is zero at
(a) the highest point of its path
(b) the lowest point of its path
(c) the middle point of its path

34. In a circus a rider rides in circular track of radius R in the
vertical plane. The minimum velocity at highest point of track
will be
(a) √(2gR) (b) 2gR (c) √(3gR) (d) √(gR)

35. A ball is thrown upwards and it returns to ground describing a
parabolic path. Which of the following remains constant?
(a) kinetic energy of the ball
(b) speed of the ball
(c) the horizontal component of velocity
(d) the vertical component of momentum

36. The dimensions of gravitational constant G are
(a) [MLT-2] (b) [ML3T-2] (c) [M-1L3T-2] (d) [M-1LT-2]

37. A machine gun fires 20g bullet at the rate of 10 per second
with a speed of 500 ms-1. If the mass of the gun is 10kg, the
force required to hold the gun in position is
(a) 10 N (b) 100 N (c) 1000 N (d) 10 dynes

38. A body is released from a great height and falls freely towards
the earth. Another body is released from the same height
exactly one second later. Then the separation between two
bodies, 2 seconds after the release of the second body is
(a) 4.9 m (b) 9.8 m (c) 19.6 m (d) 24.5 m

39. A stone thrown vertically upwards from the top of a tower
reaches the ground with speed 30 m/s. If the initial speed is
10 m/s, the height of the tower is
(a) 10 m (b) 100 m (c) 40 m (d) 800 m

40. A box is dragged across a floor by a rope which makes an angle
600 with the horizontal. The tension in the rope is 200N, while
the box is dragged 20m. The work done is
(a) 200 J (b) 3464 J (c) 2000 J (d) 346.4 J

41. The density of a cube is measured by measuring mass and the
length of its side. If the maximum errors in the measurement of
mass and length are 3% and 2% respectively, the maximum
error in the measurement of the density is
(a) 1% (b) 5% (c) 7% (d) 9%

42. A uniform metre scale initially in the vertical direction is turned
through 450 with bottom end fixed. The percentage fall in its
potential energy
(a) 29% (b) 42% (c) 25% (d) 33%

43. The centre of mass of a right circular cone of height h is
(a) on the axis at a distance h/4 from the base of the cone
(b) on the axis at a distance h/3 from the base of the cone
(c) on the axis at a distance h/2 from the base of the cone
(d) on the base of the cone at its distance

44. The unit of energy is
(a) J/S (b) Watt × Day (c) Kilowatt (d) g. cm/s2

45. The measured mass and volume of a body are 22.42gm and
4.7 cm2 respectively with possible error 0.01gm and 0.1 cm3.
The maximum error in density is
(a) 0.2% (b) 2% (c) 5% (d) 10%

46. Railway tracks are banked on curves so that:
(a) the train may not fall down inwards
(b) the weight of the train may be reduced
(c) necessary centripetal force may be obtained from the
horizontal component of the normal reaction due to the track
(d) no frictional force may be produced between the wheels
and the track

47. A body travels three equal distances with speeds 10 m/s,
20 m/s and 30 m/s respectively. The average speed will be
(a) 20 m/s (b) 16.36 m/s (c) 31.20 m/s (d) 25.12 m/s

48. A body moves a distance of 10m along a straight line under the
action of a force of 5N. If the work done is 25J, the angle
which the force makes with the direction of motion of the body
(a) 00 (b) 300 (c) 600 (d) 900

49. What will happen if a stream of air is blown through a tube
under one of the pans of a physical balance in equilibrium?
(a) the pan will go up
(b) the pan will go down
(c) the pan will remain unaffected
(d) the pan may go up or down depending upon the metal of
which the pan is made

50. A car covers the first half of the distance between two places
at a speed of 40 km/hr and the second half at 60 km/hr. Then
the average speed of the car is
(a) 50 km/hr (b) 48 km/hr (c) 100 km/hr (d) 55 km/hr


1 B 11 B 21 C 31 C 41 D
2 A 12 A 22 C 32 A 42 A
3 A 13 A 23 A 33 C 43 A
4 C 14 B 24 D 34 D 44 B
5 A 15 C 25 A 35 C 45 B
6 D 16 C 26 C 36 C 46 C
7 B 17 A 27 B 37 B 47 B
8 C 18 A 28 A 38 D 48 C
9 A 19 B 29 D 39 C 49 B
10 C 20 D 30 A 40 C 50 B
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