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•Spheres A and B of uniform density have masses 1 kg and 100 kg respectively. Their centres are separated by 100 m. (i) Find the gravitational force between them. (ii) Find the gravitational force on A due to the earth. (iii) Suppose A and B are initially at rest and A can move freely towards B. What will be the velocity of A one second after it starts moving towards B? How will this velocity change with time? How much time will A take to move towards B by 1 cm? (iv) If A begins to fall, starting from rest, due to the earth's downward pull, what will be its velocity after one second? How much time will it take to fall through 1 cm? [M(earth) = 6 x 1024 kg, earth) = 6400 km]
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