**APEX INSTITUTE SCIENCE **

**ASSIGNMENT**

1. Calculate the gravitational force between a 10-kg ball and a 20-kg ball placed at a separation of 5 m.

2. Three balls A, B and C are kept in a straight line. The separation between A and C is 1 m, and B is placed at the midpoint between them. The masses of A, B, C are 100 g, 200 g and 300 g respectively. Find the net gravitational force on (a) A, (b) B, and (c) C.

3. A particle of mass m1 is kept at x = 0 and another of mass m2 at x = d. When a third particle is kept at x = d/4, it experiences no net gravitational force due to the two particles. Find m2/m1.

4. The acceleration due to gravity near the earth's surface is 9.8 m/s2, and the earth's radius is 6,400 km. From this data calculate the mass of the earth. Use any universal constant if required.

5. Two particles of mass 200 g each are placed at a separation of 10 cm. Assume that the only forces acting on them are due to their gravitational attraction. Find the acceleration of each when they are allowed to move.

6. A particle weighs 120 N on the surface of the earth. At what height above the earth's surface will its weight be 30 N? Radius of the earth = 6,400 km.

7. Suppose the earth shrinks such that its radius decreases to half the present value. What will be the acceleration due to gravity on the surface of the earth?

8. A body weighs 120 N on the earth. Find its approximate weight on the moon.

9. Calculate the value of the acceleration due to gravity at a place 3,200 km above the surface of the earth.

10. The acceleration due to gravity at a place is 0.2 m/s 2. Find its height above the earth's surface.

11. As one moves to a place 3,200 km above the earth's surface, the acceleration due to gravity reduces to 4/9 of its value at the earth's surface. Calculate the radius of the earth from this data.

12. A ball is dropped from a cliff. Find (a) its speed 2 s after it is dropped, (b) its speed when it has fallen through 78.4 m, and (c) the time taken in falling through 78.4 m.

13. A ball is thrown upwards with a speed of 39.2 m/s. Calculate (a) the maximum height it reaches, and (b) the time taken in reaching the maximum height.

14. A ball thrown upwards takes 4 s to reach the maximum height. Find (a) the initial speed with which it was thrown, and (b) the maximum height reached.

15. An object thrown upwards reaches the highest point in 5.0 s. Find the velocity with which it was thrown.

16. A stone thrown upwards attains a maximum height of 19.6 m. Find the velocity with which it was thrown.

17. A body is thrown upwards with a velocity of 20 m/s. How much time will it take to return to its original position?

18. A ball is dropped from a height 2.50 m above the floor, (a) Find the speed v with which it reaches the floor, (b) The ball now rebounds. The speed of the ball is decreased to 3u/4 due to this collision. How high will the ball rise?

19. A stone is dropped from a cliff at 2:30:30 p.m. (hour: minute:second). Another stone is dropped from the same point at 2:30:31 p.m. Find the separation between the stones at (a) 2:30:31 p.m., (b) 2:30:35 p.m.

20. A ball is thrown upwards from the surface of the moon with a velocity of 19.6 m/s. (a) How much time will it take to attain the maximum height? (b) How high will it go?

21. A flowerpot drops from the edge of the roof of a multistoried building. Calculate the time taken by the pot to cross a particular distance AB of height 2.9 m, the upper point A being 19.6 m below the roof.

22. A wicket keeping glove is dropped from a height of 40 m and simultaneously a ball is thrown upwards from the ground with a speed of 40 m/s. When and where do they meet?

23. A boy on a 78.4-m-high cliff drops a stone. One second later, he throws another stone downwards with some speed. The two stones reach the ground simultaneously. Find the speed with which the second stone was thrown.

Answers

1.5.34 x 10"10 N

2. (a) 7.34 x 10 "12 N towards C (b) 1.07 x 10 "n N towards C (c) 1.80 x 10 N towards A

3.9 4. 6.02x10 24 kg 5.1.33 x 10 ~9 m/s2 6.6,400 km

7.39.2 m/s2 8.20 N 9.4.36 m/s2 10.6Re = 38,400 km

11.6,400 km 12. (a) 19.6 m/s (b) 39.2 m/s (c) 4 s 13. (a) 78.4 m (b) 4 s

14. (a) 39.2 m/s (b) 78.4 m 15.49 m/s . 16.19.6 m/s

17.4.08 s 18. (a) 7 m/s (b) 1.4 m 19. (a) 4.9 m (b) 44.1 m 20. (a) 12 s (b) 117.6 m

21.1/7s 22.1 s after the glove is dropped, 35.1 m above the ground

23.11.43

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