2022Flame Institute

2. When a body is stationary

(a) There is no force acting on it (b) The force acting on it is not in contact with it (c) The combination of forces acting on it balances each other (d) The body is in vacuum Ans . c …

A 10kg mass moves along x-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from x=0 to x=8 cm

(a) 8×10-2 joules (b) 16×10-2 joules (c) 4 ×10-4 joules (d) 1.6 ×10-3 joules Answer: A (21)

3. Two forces of magnitude F have a resultant of the same magnitude F. The angle between the two forces is

(a) 45° (b) 120° (c) 150° (d) 60° Ans . b (8)

Adjacent figure shows the force-displacement graph of a moving body, the work done in displacing body from x =0 to x=35 m is equal to

(a) 50 J (b) 25 J (c) 287.5 J (d) 200 J Answer:c (15)

4. Two forces with equal magnitudes F act on a body and the magnitude of the resultant force is F/3. The angle between the two forces is

(a) c0s -1 (-17/18) (b) cos -1 (-1/3) (c) cos -1 (2/3) (d) cos (8/9) Ans. a (61)

Let F be the force acting on a particle having position vector r vector and T vector be the torque of this force about the origin. Then

(a) r vector X T vector=0 and F vector X T vector =0 (b) r vector X T vector = 0 and F vector x T vector not equal to Zero (c) r vector X T vector not equal to …

28. Let A vector be a unit vector along the axis of rotation of a purely rotating body and B vector be a unit vector along the velocity of a particle P of the body away from the axis. The value of A vector X B vector is

(a) 1 (b) – 1 (c) 0 (d) None of these Ans. c (7)

A toy car of mass 5 kg moves up a ramp under the influence of force F plotted against displacement x. The maximum height attained is given by

(a) ymax=20m (b) ymax= 15m (c) ymax= 11m (d) ymax = 5m Answer: C (14)

27. When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many more rotations will it make before coming to rest (Assume uniform angular retardation)

(a) 36 (b) 24 (c) 18 (d) 12 Ans. d (16)

27. A jet engine works on the principle of

(a) Conservation of mass (b) Conservation of energy (c) Conservation of linear momentum (d) Conservation of angular momentum Ans. c (13)

25. A rigid body is rotating with variable angular velocity (a-bt) at any instant of time t. The total angle subtended by it before coming to rest will be (a and b are constants)

(a) (a-b)a/2 (b) a2/2b (c) a2-b2/2b (d) a2-b2/2a Ans. b (11)

26. At a certain instant of time the mass of a rocket going up vertically is 100 kg. If it is ejecting 5 kg of gas per second at a speed of 400 m/s, the acceleration of the rocket would be (taking g = 10 m/s ^2

(a) 20m/s 2 (b) 10m/s 2 (c) 2 m/s 2 (d) …

25. A rocket can go vertically upwards in earth’s atmosphere because

a) It is lighter than air (b) Of gravitational pull of the sun (c) It has a fan which displaces more air per unit time than the weight of the rocket (d) Of the force exerted on the rocket by …

24. A bullet mass 10 gm is fired from a gun of mass 1kg. If the recoil velocity is 5 m/s, the velocity of the muzzle is

(a) 0.05 m/s (b) 5 m/s (c) 50 m/s (d) 500 m/s Ans. d (3)

24. A sphere is rotating about a diameter

(a) The particles on the surface of the sphere do not have any linear acceleration (b) The particles on the diameter mentioned above do not have any linear acceleration (c) Different particles on the surface have different angular speeds (d) …

23. A bullet of mass 0.1 kg is fired with a speed of 100 m/sec, the mass of gun is 50 kg. The velocity of recoil is

(a) 0.2 m/sec (b) 0.1 m/sec (c) 0.5 m/sec (d) 0.05 m/sec Ans. a (11)

23. The planes of two rigid discs are perpendicular to each other. They are rotating about their axes. If their angular velocities are 3 rad/sec and 4 rad/sec respectively, then the resultant angular velocity of the system would be

(a) 1 rad/sec (b) 7 rad/sec (c) 5 rad/sec (d) √12 rad/sec Ans. c (561)

A bullet is fired from a gun. The force on the bullet is given by f = 600- 2 x 10 5 t where F is in newtons and t in seconds. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet

(a) 9 Ns (b) Zero (c) 0.9 Ns (d) 1.8 Ns ans. c (23)

21. A body of mass 0.25 kg is projected with muzzle velocity 100ms ^-1 from a tank of mass 100 kg. What is the recoil velocity of the tank

(a) 5 ms -1 (b) 25ms -1 (c) 0.5 ms -1 (d) 0.25 ms -1 ans. …

22. A particle starts rotating from rest. Its angular displacement is expressed by the following equationθ =0.025t square-0.1t where θ is in radian and t is in seconds. The angular acceleration of the particle is

(a) 0.5 rad/sec2 at the end of 10 sec (b) 0.3 rad/sec2 at the end of 2 sec (c) 0.05 rad/sec2 at the end of 1 sec (d) Constant 0.05 rad/sec2 Ans. d (25)

A set of n identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is L. The block at one end is given a speed v towards the next one at time t=0 . All collisions are completely inelastic, then

(a) The last block starts moving at t=(n-1)L/v (b) The last block starts moving at t=n(n-1)L/2v (c) The centre of mass of the system will have a final speed v (d) The centre of mass of the system will have …

A particle P moving with speed v undergoes a head -on elastic collision with another particle Q of identical mass but at rest. After the collision

(a) Both P and Q move forward with speed v/2 (b) Both P and Q move forward with speed v/√2 (c) P comes to rest and Q moves forward with speed v (d) P and Q move in opposite directions …

A body of mass m moving with velocity v collides head on with another body of mass 2m which is initially at rest. The ratio of K.E. of colliding body before and after collision will be

(a) 1 : 1 (b) 2 : 1 (c) 4 : 1 (d) 9 : 1 Answer: d (6)

Consider elastic collision of a particle of mass m moving with a velocity u with another particle of the same mass at rest. After the collision the projectile and the struck particle move in directions making angles θ1 and θ2 respectively with the initial direction of motion. The sum of the angles θ1+θ2, is

(a) 45° (b) 90° (c) 135° (d) 180° Answer:b (8)

Two particles of masses m1 and m2 in projectile motion have velocities

(a) Zero (b) (m1+m2)gt0 (c) 2(m1+m2)gt0 (d) 1/2(m1+m2)gt0 Answer: c (12)

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 …