LEVEL – I

Q:1. A stone is released from an elevator going up with acceleration 5 m/s^{2} . The acceleration of the stone after the release is:

(A) 5 ms^{-2 }

(B) 4.8 ms^{-2} upward

(C) 4.8 down ward

(D) 9.8 ms^{-2} down ward

Q:2. The locus of a projectile relative to another projectile is a

(A) straight line

(B) circle

(C ) ellipse

(D) parabola

Q:3. A car accelerates from rest at constant rate of 2 m/s^{2} for some time. Then its retards at a constant rate of 4 m/s^{2} and comes to rest. What is the maximum speed attained by the car if it remains in motion for 3 seconds

(A) 2 m/s

(B) 3 m/s

(C) 4 m/s

(D) 6 m/s

Q:4. The co-ordinates of a moving particle at any time t are given by x = ct^{2} and y = bt^{2}. The speed of the particle is given by:

(A) 2t (c + b)

(B) 2t√(c^{2}-b^{2})

(C) t√(c^{2}-b^{2})

(D) 2t√(c^{2}-b^{2})

Q:5. A particle parallel to x-axis as shown in the figure such that at all instant the y axis component of its position vector is constant and is equal to ‘b’. The angular velocity of the particle about the origin is

(A) v/b

(B) (v/b)Sinθ

(C) (v/b) Sin^{2}θ

(D) vb

Q:6. A particle is projected vertically upwards and it attains maximum height H. If the ratio of times to attain height h(h < H) is 1/3, then h equals

(A) 2/3. H

(B) 3/ 4. H

(C) 4/3 . H

(D) 3/2. H

Q:7. A boy B drags a wedge A by an in extensible string passing over the pulleys 1,2,3 & 4 as shown in the figure . If all the pulleys are smooth and the boy walks with constant velocity of magnitude v, the magnitude of relative velocity between the boy and the wedge is equal to

(A) v

(B) 2v

(C) 1.5v

(D) 1.25v

Q:8. A swimmer wishes to reach directly opposite bank of a river, flowing with velocity 8 m/s. The swimmer can swim 10 m/s in still water. The width of the river is 480 m. Time taken by him to do so:

(A) 60 sec

(B) 48 sec

(C) 80 sec

(D) None of these

Q:9. A man can swim at a speed of 5 km/h w.r.t. water. He wants to cross a 1.5 km wide river flowing at 3 km/h. He keeps himself always at an angle of 60° with the flow direction while swimming. The time taken by him to cross the river will be

(A) 0.25 hr.

(B) 0.35 hr.

(C) 0.45 hr.

(D) 0.55 hr.

Q:10. A disc of radius R is rotating inside a room A boy standing near the rim of the disc, finds the water droplets falling from the ceiling is always hitting on his head. As one drop hits his head the next one starts from the ceiling. If height of the roof above his head is H. Angular velocity of disc is:

(A) $ \displaystyle \pi \sqrt{\frac{2 g R}{H^2}} $

B) $ \displaystyle \pi \sqrt{\frac{2 g H}{R^2}} $

(C) $ \displaystyle \pi \sqrt{\frac{2 g }{H}} $

(D) $ \displaystyle 2\pi \sqrt{\frac{2 g }{H}} $

__ANSWER:__

1.(D) 2. (A) 3. (C) 4. (D) 5. (C) 6. (C) 7. (D) 8. (C) 9. (B) 10. (C)

Q:11. The acceleration-time graph of a particle moving along a straight line is as shown in figure. At what time the particle acquires its initial velocity?

(A) 12 sec.

(B) 5 sec.

(C) 8 sec.

(D) 16 sec.

Q:12. What are the speeds of two objects if they move uniformly towards each other, they get 4m closer in each second and if they move uniformly in the same direction with the original speeds they get 4m closer in each 10 sec ?

(A) 2.8 m/s and 1.2 m/s

(B) 5.2 m/s and 4.6 m/s

(C) 3.2 m/s and 2.1 m/s

(D) 2.2 m/s and 1.8 m/s

Q:13. From the top of a tower, a stone is thrown up. It reaches the ground in 5 sec. A second stone is thrown down with the same speed and reaches the ground in 1sec. A third stone is released from rest and reaches the ground in

(A) 3 sec.

(B) 2 sec.

(C) √5 sec.

(D) 2.5 sec.

Q:14. A particle has an initial velocity of (3 i^{^}+ 4j^{^} )m/s and a constant acceleration of (4i^{^}-3j^{^} ) m/s^{2}. Its speed after one second will be equal to

(A) 0

(B) 10 m/sec

(C) 5√2 m/sec

(D) 25 m/sec

Q:15. A balloon starts rising from the ground with an acceleration of 1.25 m/s^{2}. After 8 seconds, a stone is released from the balloon. After releasing, the stone will

(A) cover a distance of 40 m till it strikes the ground.

(B) have a displacement of 50 m till it reaches the ground

(C) reach the ground in 4 seconds.

(D) begin to move down instantaneously

Q:16. Two balls are dropped from the top of a high tower with a time interval of t0 second, where t0 is smaller than the time taken by the first ball to reach the floor which is perfectly inelastic. The distance S between the two balls, plotted against the time lapse ‘t’ from the instant of dropping the second ball is best represented by

Q:17. The K.E. (K) of a particle moving along a circle of radius R depends on the distance covered s as K = a s^{2}. The force acting on particle is

(A) $ \displaystyle \frac{2 a s^2 }{R} $

(B) $ \displaystyle \frac{2 a s }{(1 + \frac{s^2}{R})^{1/2}} $

(C) $ \displaystyle 2 a s(1+\frac{s^2}{R^2})^{1/2} $

(D) none of these.

Q:18. Two particles P and Q start from rest and move for equal time on a straight line. Particle P has an acceleration of X m/s^{2} for the first half of the total time and 2x m/s^{2} for the second half. Particle Q has an acceleration of 2X m/s^{2} for the first half of the total time and X m/s^{2} for the second half. Which particle has covered larger distance?

(A) Both have covered the same distance

(B) P has covered the larger distance

(C) Q has covered the larger distance

(D) data insufficient

Q:19. A particle is moving in a circle of radius R in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at t = 0 is v_{o} the time taken to complete the first revolution is

(A) R/v_{o}

(B) v_{o} /R

(C) R/v_{o} (1 – e-^{2π})

(D) R/v_{o} (e-^{2π})

Q:20. A motor boat of mass m moves along a lake with velocity v_{o} . At t = 0, the engine of the boat is shut down. Resistance offered to the boat is equal to σv. What is the total distance covered till it stops completely?

(A) mv_{o}/σ

(B) 3mv_{o}/2σ

(C) mv_{o}/2σ

(D) 2 mv_{o}/σ

__ANSWER:__

11. (C) 12. (D) 13. (C) 14. (C) 15. (C) 16. (D) 17. (C) 18. (C) 19. (C) 20. (A)