IX CBSE Physics Numerical For Chapter: Gravitation .Olympiad Practice |

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 ^{12} N towards C (c) 1.80 x 10 ^{12} 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/s ^{2 } 8. 20 N |

9. 4.36 m/s ^{2 }10. R_{e} = 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, |

23. 1 m above the ground 24. 11.43 |