If the distance between two bodies is increased by a factor of 5, (i) by what factor will the gravitational force change if the masses are kept consant ? (ii) by what factor will the mass of one of them have to be altered, keeping the other mass the same, to maintain the same gravitational force between the two bodies.?

Explanation

If the distance between two bodies is increased by a factor of 5,
(i) The gravitaional force between the bodies will decreases by a factor of 25 if the masses of the bodies are kept constant.
(ii) the mass of one of them will have to be increased by a factor of 25, keeping the mass of the other body the same, to maintain the same gravitational force between the two bodies.
Gravitational force `Fprop (1)/(r^(2)) and F prop m_(1)m_(2).`