Question

The distance between two bodies is doubled. How is the magnitude of gravitational force between them affected?

Answer 1

Let $m_1$ and $m_2$ be the masses of the respective bodies.

Let the distance between the two bodies be $d$.

Gravitational force between them initially $F=\frac{G{m}_1{m}_2}{d^2}$

Now the distance between them is doubled i.e. $d^{\prime }=2d$

New gravitational force acting between them $F^{\prime }=\frac{G{m}_1{m}_2}{(d^{\prime }{)}^2}$

$\therefore$ $F^{\prime }=\frac{G{m}_1{m}_2}{4d^2}=\frac{F}{4}$

Thus gravitational force gets reduced by a factor of $4$.