9th Standard Chapter 9 Gravitation NCERT Solution

Exercises with Answers

1. How does the force of gravitation between two objects change when the distance between them is reduced to half?
   Answer: The force becomes four times because gravitational force is inversely proportional to the square of the distance between the objects.
2. Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?
   Answer: Because the acceleration due to gravity is the same for all objects irrespective of their masses, so both fall at the same rate.
3. What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 x 10²⁴ kg and radius of the earth is 6.4 x 10⁶ m.)
   Answer: Using F = GMm/R², F = (6.67 x 10^-11 x 6 x 10²⁴ x 1) / (6.4 x 10⁶)² = 9.8 N approximately.
4. The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?
   Answer: The force is the same due to Newton’s third law of motion (action and reaction are equal and opposite).
5. If the moon attracts the earth, why does the earth not move towards the moon?
   Answer: Earth does move towards the moon, but due to its much larger mass, the movement is negligible.
6. What happens to the force between two objects, if
   1. the mass of one object is doubled?
   2. the distance between the objects is doubled and tripled?
   3. the masses of both objects are doubled?
   Answer:
   1. Force will double.
   2. Force will become one-fourth when doubled and one-ninth when tripled.
   3. Force will become four times as both masses are doubled.
7. What is the importance of universal law of gravitation?
   Answer: It explains the motion of planets, the tides, and the existence of gravity everywhere in the universe.
8. What is the acceleration of free fall?
   Answer: The acceleration of free fall is 9.8 m/s² on the surface of the earth.
9. What do we call the gravitational force between the earth and an object?
   Answer: Weight of the object.
10. Amit buys few grams of gold at the poles as per the instruction of one of his friends. He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why? (Hint: The value of g is greater at the poles than at the equator.)
    Answer: No, because the weight will be slightly less at the equator due to the lower value of g.
11. Why will a sheet of paper fall slower than one that is crumpled into a ball?
    Answer: Due to air resistance acting more on the flat sheet than on the crumpled ball.
12. Gravitational force on the surface of the moon is only ¹/₆ as strong as gravitational force on the earth. What is the weight in newtons of a 10 kg object on the moon and on the earth?
    Answer: Weight on earth = 10 kg x 9.8 m/s² = 98 N, on the moon = 98/6 ≈ 16.3 N.
13. A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate
    1. the maximum height to which it rises.
    2. the total time it takes to return to the surface of the earth.
    Answer:
    1. H = u²/(2g) = (49)²/(2 x 9.8) = 122.5 m.
    2. Total time = 2u/g = 2 x 49/9.8 = 10 s.
14. A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity just before touching the ground.
    Answer: v = √(2gh) = √(2 x 9.8 x 19.6) = 19.6 m/s.
15. A stone is thrown vertically upward with an initial velocity of 40 m/s. Taking g = 10 m/s², find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone?
    Answer: Max height = u²/(2g) = 1600/20 = 80 m. Net displacement = 0 if it returns to the ground, total distance = 160 m.
16. Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 x 10²⁴ kg and of the Sun = 2 x 10³⁰ kg. The average distance between the two is 1.5 x 10¹¹ m.
    Answer: F = G M m / r² = (6.67 x 10^-11 x 6 x 10²⁴ x 2 x 10³⁰) / (1.5 x 10¹¹)² ≈ 3.56 x 10²² N.
17. A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculate when and where the two stones will meet.
    Answer: Let the meeting point be at height h after time t. Using equations of motion, they will meet after 4 s at a height of 20 m above the ground.
18. A ball thrown up vertically returns to the thrower after 6 s. Find
    1. the velocity with which it was thrown up.
    2. the maximum height it reaches, and
    3. its position after 4 s.
    Answer:
    1. u = g x t/2 = 9.8 x 3 = 29.4 m/s.
    2. H = u²/(2g) = 29.4²/(2 x 9.8) = 44.1 m.
    3. At 4 s, it will be on its way down, at 19.6 m above the thrower.
19. In what direction does the buoyant force on an object immersed in a liquid act?
    Answer: Upward, opposite to the direction of gravity.
20. Why does a block of plastic released under water come up to the surface of water?
    Answer: Because the density of plastic is less than water, so the buoyant force is greater than its weight.
21. An object of volume 500 cm³ is immersed in water. If the density of water is 1 g cm^-3, what will be the buoyant force on the object?
    Answer: Buoyant force = weight of displaced water = 500 g = 0.5 kg x 9.8 m/s² = 4.9 N.
22. Will the buoyant force on a piece of wood be same as the buoyant force on a piece of iron of the same volume when both are fully immersed in water? Why?
    Answer: Yes, because the buoyant force depends on the volume of fluid displaced, not on the material of the object.
23. The volume of 500 g sealed packet is 350 cm³. Will the packet float or sink in water if the density of water is 1 g cm^-3? What will be the mass of the water displaced by this packet?
    Answer: Density of packet = 500/350 ≈ 1.43 g/cm³ > 1 g/cm³, so it will sink. Mass of water displaced = 350 g.