J J Science Academy Test Paper

1. A ball is dropped from a bridge 125 meter above a river. After the ball has been falling for two second, a second ball is thrown straight down after it. What must its initial velocity be so that both hit the water at the same time? $(g=10 m / s^{2})$

1) $(39 m / s)$
2) $(55.5 m / s)$
3) $(26.7 m / s)$
4) $(19.8 m / s)$

2. A ball is dropped from a bridge 125 meter above a river. After the ball has been falling for two second, a second ball is thrown straight down after it. what is the velocity of the first ball when it hits the water? $(g=10 m / s^{2})$

1) $(50 m / s)$
2) $(69 m / s)$
3) $(55.5 m / s)$
4) $(9.8 m / s)$

3. A ball is dropped from a bridge 125 meter above a river. After the ball has been falling for two second, a second ball is thrown straight down after it. what is the velocity of the second ball? $(g=10 m / s^{2})$

1) 56.66 m/s
2) $(45.5 m / s)$
3) $(38.4 m / s)$
4) $(19.8 m / s)$

4. Two bodies of different masses $(m_{a})$ and $(m_{b})$ are dropped from two different heights, a and b . The ratio of time taken by the two to drop through these distances is

1) $(a : b)$
2) $(m_{a} / m_{b} : b / a)$
3) $(\sqrt{a} : \sqrt{b})$
4) $(a^{2} : b^{2})$

5. A body is fired vertically upwards, with a velocity $(60 m / s)$. The time intervals between the instants when it has a vertical displacement of 120 m , is

1) 6 s
2) 12 s
3) $(8 \sqrt{3} s)$
4) $(4 \sqrt{3} s)$

6. A body is fired vertically upwards, with a velocity $(60 m / s)$, the change in velocity of the body after a time interval of 5 s is

1) $(-50 \sqrt{2} m / s)$
2) $(-50 m / s)$
3) $(50 \sqrt{2} m / s)$
4) $(50 m / s)$

7. A body dropped from the top of a tower covers a distance 7 x in the last second of its journey where x is the distance covered in first second. How much time does it take to reach the ground?

1) 3 s
2) 4 s
3) 5 s
4) 6 s

8. A body, fired vertically upwards with velocity $(u)$, attains the same speed after time $(T)$. At two instants, $(t_{1})$ and $(t_{2})$, it crosses a point in its path. The $(t_{1}+t_{2}=)$

1) T
2) $(\frac{3 T}{4})$
3) $(\frac{T}{2})$
4) $(\frac{5 T}{4})$

9. A player throws a ball vertically upwards with velocity u. At highest point,

1) Both the velocity and acceleration of the ball are zero.
2) The velocity of the ball is $(u)$ but its acceleration is zero.
3) The velocity of the ball is zero but its acceleration is g.
4) The velocity of the ball is $(u)$ but its acceleration is $(g)$.

10. A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first five seconds of its motion. The height from which stone is dropped is

1) 545 m
2) 845 m
3) 645 m
4) 745 m

11. If the velocity of a body, thrown upwards, is increased by $(10 \%)$, the maximum height reached by it will increase by

1) 20%
2) $(21 \%)$
3) $(10 \%)$
4) 11

12. Two balls A and B of same masses are thrown from the top of the building. ' A ', thrown upwards with velocity v and 'B', thrown downwards with velocity v , then

1) Velocity of A is more than B at the ground.
2) Velocity of B is more than A at the ground.
3) Both A and B strike the ground with same velocity.
4) None of these

13. An elevator car, whose floor to ceiling distance is equal to 2.7 m , starts ascending with constant acceleration of $(1.2 ms^{-2})$. Two sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is

1) $(\sqrt{0.54} s)$
2) $(\sqrt{6} s)$
3) 0.7 s
4) 1 s

14. A ball is dropped from a bridge of 122.5 metre above a river. After the ball has been falling for two seconds, a second ball is thrown straight down after it. Initial velocity of second ball, so that both hit the water at the same time is

1) $(49 m / s)$
2) $(55.5 m / s)$
3) $(26.1 m / s)$
4) $(9.8 m / s)$

15. A body thrown vertically up to reach its maximum height in $(t)$ second. The total time from the time of projection to reach a point at half of its maximum height while returning (in second) is

1) $(\sqrt{2} t)$
2) $((1+\frac{1}{\sqrt{2}}) t)$
3) $(\frac{3 t}{2})$
4) $(\frac{t}{\sqrt{2}})$

16. Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projection in their downward motion, with

1) the heavier ball having more speed.
2) the lighter ball having more speed.
3) both having the same speed.
4) can not be predicted as actual height achieved is not given.

17. A body, of mass M , is thrown upwards with, from ground, with velocity u . The average acceleration of the body, during the time t in air is

1) $(g / 2)$
2) g
3) $(3 g / 4)$
4) $(2 g / 3)$

18. A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first five seconds of its motion. The height from which stone is dropped is

1) 545 m
2) 845 m
3) 645 m
4) 745 m

19. A body, fired vertically upwards, reaches a maximum height H in time T . The distance it covers in time $(3 T / 2)$ is

1) $(\frac{3 H}{2})$
2) $(\frac{7 H}{4})$
3) $(\frac{3 H}{4})$
4) $(\frac{5 H}{4})$

20. When a ball is thrown up vertically with velocity $(v_{0})$, it reaches a maximum height of ' h '. If one wishes to triple the maximum height, then the ball should be thrown with velocity

1) $(\sqrt{3} v_{0})$
2) $(3 v_{0})$
3) $(9 v_{0})$
4) $(\frac{3 v_{0}}{2})$

21. A body rolls down a stair case of 5 steps. Each step has height 0.1 m and width 0.1 m . With what velocity will the body reach the bottom?

1) $(5 \sqrt{2} m / s)$
2) $(\frac{1}{\sqrt{2}} m / s)$
3) $(2 \sqrt{2} m / s)$
4) $(\sqrt{\frac{5}{2}} m / s)$

22. A player throws a ball vertically upwards with velocity u. At highest point,

1) Both the velocity and acceleration of the ball are zero.
2) The velocity of the ball is u but its acceleration is zero.
3) The velocity of the ball is zero but its acceleration is g.
4) The velocity of the ball is u but its acceleration is g.

23. Water drops fall from the roof of a building 20 m high at regular intervals of time. The first drop reaching the ground at the same instant fifth drop starts its fall. The time between two successive drops is $(g=10 m / s^{2})$

1) 2 s
2) 1 s
3) 0.5 s
4) 1.5 s

24. If the velocity of a body, thrown upwards, is increased by $(10 \%)$, the maximum height reached by it will increase by

1) $(20 \%)$
2) $(21 \%)$
3) $(10 \%)$
4) $(11 \%)$

25. A body is dropped from the top of a tower, 30 m high. At the same time a body is fired from the ground, vertically upward, along the same line, with a speed of $(10 m / s)$. The time after which they will collide with each other is

1) 0.5 s
2) 1.5 s
3) 2 s
4) 3 s

26. A ball thrown up from the ground is observed at a certain height after times 4 s and 6 s . If the acceleration due to gravity is $(10 ms^{-2})$, the velocity of throw is

1) $(50 ms^{-1})$
2) $(100 ms^{-1})$
3) $(25 ms^{-1})$
4) $(75 ms^{-1})$