May, 2022Flame Institute

15. A vessel at rest explodes into three pieces. Two pieces having equal masses fly off perpendicular to one another with the same velocity 30 meter per second. The third piece has three times mass of each of other piece. The magnitude and direction of the velocity of the third piece will be

(a) 10√2 m/second and 135° from either (b) 10√2 m/second and 45° from either (c) 10/√2 m/second and 135° from either (d) 10/√2 m/second and 45° from either Answer: a (3)

A shell is fired from a cannon with velocity v m/sec at an angle θ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed in m/sec of the other piece immediately after the explosion is

(a) 3v cosθ (b) 2v cosθ (c) 3/2v cosθ (d) √3/2 cosθ Answer: a (7)

A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

(a) t1/2 (b) t3/4 (c) t3/2 (d) t2 Answer: …

Consider the following two statements 1. Linear momentum of a system of particles is zero 2. Kinetic energy of a system of particles is zero Then

(a) 1 implies 2 and 2 implies 1 (b) 1 does not imply 2 and 2 does not imply 1 (c) 1 implies 2 but 2 does not imply 1 (d) 1 does not imply 2 but 2 implies 1 …

An open knife edge of mass ‘m’ is dropped from a height ‘h’ on a wooden floor. If the blade penetrates upto the depth ‘d’ into the wood, the average resistance offered by the wood to the knife edge is

(a) mg (b) mg (1-h/d) (c) mg (1+h/d) (d) mg(1+h/d)2 Answer: c (5)

The kinetic energy acquired by a mass m in travelling a certain distance d starting from rest under the action of a constant force is directly proportional to

(a) √m (b) Independent of m (c) 1/√m (d) m …

A particle free to move along the x-axis has potential energy given by U(x) = K [1-exp(-x)2] for – ∞<–x<–+∞, where k is a positive constant of appropriate dimensions. Then

(a) At point away from the origin, the particle is in unstable equilibrium (b) For any finite non-zero value of x, there is a force directed away from the origin (c) If its total mechanical energy is k/2, it has …

A ball hits the floor and rebounds after inelastic collision. In this case

(a) The momentum of the ball just after the collision is the same as that just before the collision (b) The mechanical energy of the ball remains the same in the collision (c) The total momentum of the ball and …

A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is

(a) MgL (b) MgL/3 (c) MgL/9 (d) MgL/18 Answer: D (6)

If W1, W2 ,and W3 represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W1, W2 and W

(a) W1>W2>W3 (b) W1=W2=W3 (c) W1<W2<W3 (d) W2 >W1>W3 Answer: b (8)

A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to -K/r2 , where K is a constant. The total energy of the particle is

a) K/2r (b) – (K/2r) (c) -(K/r) (d) K/r Answer: b (39)

7. A 100 g iron ball having velocity 10 m/s collides with a wall at an angle 30° and rebounds with the same angle. If the period of contact between the ball and wall is 0.1 second, then the force experienced by the wall is

(a) 10 N (b) 100 N (c) 1.0 N (d) 0.1 N answer : a (6)

The displacement x of a particle moving in one dimension under the action of a constant force is related to the time t by the equation t=√x+3 , where x is in meters and t is in seconds. The work done by the force in the first 6 seconds is

(a) 9 J (b) 6 J (c) 0 J (d) 3 J Answer: C (5)

6. If a force of 250 N act on body, the momentum acquired is 125 kg-m/s. What is the period for which force acts on the body

(a) 0.5 sec (b) 0.2 sec (c) 0.4 sec (d) 0.25 sec answer : a (29)

5. A wagon weighing 1000 kg is moving with a velocity 50km/h on smooth horizontal rails. A mass of 250 kg is dropped into it. The velocity with which it moves now is

(a) 2.5 km/hour (b) 20 km/hour (c) 40 km/hour (d) 50 km/hour answer : c (4)

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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Month: May 2022

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