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A force F = -K(yi+xj) (where K is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the force F on the particles is

(a) -2 Ka2 (b) 2 Ka2 (c) – Ka2 (d) Ka2 Answer: …

4. In which of the following cases forces may not be required to keep the

(a) Particle going in a circle (b) Particle going along a straight line (c) The momentum of the particle constant (d) Acceleration of the particle constant ANSWER: c (9)

3. A rocket has a mass of 100 kg. 90% of this is fuel. It ejects fuel vapours at the rate of 1 kg/sec with a velocity of 500 m/sec relative to the rocket. It is supposed that the rocket is outside the gravitational field. The initial upthrust on the rocket when it just starts moving upwards is

(a) Zero (b) 500 N (c) 1000 N (d) 2000 N ANSWER : b (10)

A lorry and a car moving with the same K.E. are brought to rest by applying the same retarding force, then

(a) Lorry will come to rest in a shorter distance (b) Car will come to rest in a shorter distance (c) Both come to rest in a same distance (d) None of the above Answer: C (6)

2. A player caught a cricket ball of mass 150 gm moving at a rate of 20 m/s. If the catching process be completed in 0.1 s, then the force of the blow exerted by the ball on the hands of the player is

(a) 0.3 N (b) 30 N (c) 300 N (d) 3000 N ANSWER : b (6)

1. A jet plane flies in the air because

(a) The gravity does not act on bodies moving with high speeds (b) The thrust of the jet compensates for the force of gravity (c) The flow of air around the wings causes an upward force, which …

If g is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass m raised from the surface of earth to a height equal to the radius of the earth R, is

(a) 1/2 mgR (b) 2 mgR (c) mgR (d) 1/4 mgR Answer: A (5)

19. Two particles having mass ‘M’ and ‘m’ are moving in circular paths having radii R and r. If their time periods are same then the ratio of their angular velocities will be

(a) r/R (b) R/r (c) 1 (d) √R/r Ans. c (8)

18. A particle B is moving in a circle of radius a with a uniform speed u. C is the centre of the circle and AB is diameter. The angular velocity of B about A and C are in the ratio

(a) 1 : 1 (b) 1 : 2 (c) 2 : 1 (d) 4 : 1 Ans. b (13)

17. A wheel is rotating at 900 r.p.m. about its axis. When the power is cut-off, it comes to rest in 1 minute. The angular retardation in radian/s2 is

(a) π/2 (b) π/4 (c) π/6 (d) π/8 Ans. a (5)

16. A car is moving at a speed of 72 km/hr. the diameter of its wheels is 0.5 m. If the wheels are stopped in 20 rotations by applying brakes, then angular retardation produced by the brakes is

(a) – 25.5 rad/s2 (b) – 29.5 rad/s2 (c) – 33.5 rad/s2 (d) – 45.5 rad/s2 Ans. a (10)

15. A flywheel gains a speed of 540 r.p.m. in 6 sec. Its angular acceleration will be

(a) 3 pi rad/sec2 (b) 9 pi rad/sec2 (c) 18 pi rad/sec2 (d) 54 pi rad/sec2 Ans. a (42)

14. The angular speed of a fly–wheel making 120 revolution/minute is

(a) π rad/sec (b) 2π rad/sec (c) 4 π rad/sec (d) 4π2 rad/sec Ans. c (25)

13. In rotational motion of a rigid body, all particle move with

(a) Same linear and angular velocity (b) Same linear and different angular velocity (c) With different linear velocities and same angular velocities (d) With different linear velocities and different angular velocities Ans.c (7)

12. Two particles of masses 1 kg and 3 kg move towards each other under their mutual force of attraction. No other force acts on them. When the relative velocity of approach of the two particles is 2m/s, their centre of mass has a velocity of 0.5 m/s. When the relative velocity of approach becomes 3 m/s, the velocity of the centre of mass is

(a) 0.5 m/s (b) 0.75 m/s (c) 1.25 m/s (d) Zero Ans.a (11)

11. Three identical spheres, each of mass 1 kg are placed touching each other with their centres on a straight line. Their centres are marked K, L and M respectively. The distance of centre of mass of the system from K is

(a) (KL+KM+LM)/3 (b) (KL+KM)/3 (C) (KL+LM)/3 (d) (KM+LM)/3 Ans. b (34)

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