Question

What happens to the gravitational force between two objects, if
$\left(i\right)$ The mass of one object is doubled?
$\left(ii\right)$ The distance between the objects is doubled and tripled?
$\left(iii\right)$ The masses of both objects are doubled?
Give reasons in each case

Answer 1

Gravitational force $F=\frac{G{m}_1{m}_2}{r^2}$

Case $\left(i\right)$ : Mass of one object is doubled i.e $m_1^{\prime }=2m_1$

$\therefore$ $F^{\prime }=\frac{G\left(2m_1\right)m_2}{r^2}$ $⟹F^{\prime }=2F$

Thus gravitational force gets also doubled

Case $\left(ii\right)$ : Distance between the objects is doubled i.e $r^{\prime }=2r$

$\therefore$ $F^{\prime }=\frac{G{m}_1{m}_2}{(2r{)}^2}$ $⟹F^{\prime }=\frac{F}{4}$

Thus gravitational force gets reduced by $4$ times.

Distance between the objects is tripled i.e $r^{\prime }=3r$

$\therefore$ $F^{\prime }=\frac{G{m}_1{m}_2}{(3r{)}^2}$ $⟹F^{\prime }=\frac{F}{9}$

Thus gravitational force gets reduced by $9$ times.

Case $\left(iii\right)$ : Mass of both the objects are doubled i.e $m_1^{\prime }=2m_1$ and $m_2^{\prime }=2m_2$

$\therefore$ $F^{\prime }=\frac{G\left(2m_1\right)\left(2m_2\right)}{r^2}$ $⟹F^{\prime }=4F$

Thus gravitational force becomes $4$ times.