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GRAVITATION NUMERICALS, 1. How does the force of gravitation between two objects change, when the distance between them is reduced to half?, 2. 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 ×, 1024 kg and radius of the earth is 6.4 × 106m.), 3. What happens to the force between two objects, if, (i) The mass of one object is doubled?, (ii) The distance between the objects is doubled and tripled?, (iii) The masses of both objects are doubled?, 4. 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?, 5. A ball is thrown vertically upwards with a velocity of 49 m/s., Calculate, (i) The maximum height to which it rises,, (ii) The total time it takes to return to the surface of the earth., 6. A stone is released from the top of a tower of height 19.6 m., Calculate its final velocity just before touching the ground., 7. 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?, 8. Calculate the force of gravitation between the earth and the, Sun, given that the mass of the earth = 6 × 1024 kg and of the, Sun = 2 × 1030 kg. The average distance between the two is 1.5, × 1011 m., 9. 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., 10., A ball thrown up vertically returns to the thrower after 6, s. Find, (a) The velocity with which it was thrown up,, (b) The maximum height it reaches, and, (c) Its position after 4s.