Gravitation- Solutions

How does the force of gravitation between two objects change when the distance between them is reduced to half

Solution:

The gravitational force of attraction between two objects is inversely proportional to the square of the distance between them. Mathematically, F ∝ 1/r2 where ‘F’ is the force and ‘r’ is the distance between them. If the distance between them is reduced to half, let ‘F1’ be the force. Hence, F1 ∝ 1/(r/2)2 => F1 ∝ 4/r2 = 4F. Thus, the force between them increases four times its initial value.