Question

Two point masses having mass $m_1$ and $m_2$ respectively. If the distance between two masses is increased by a factor of $2$. Then gravitational force:

• A. Decreases by a factor of $4$
• B. Decreases by a factor of $2$
• C. Increases by a factor of $2$
• D. increases by a factor of $4$
• E. Cannot be determined without knowing the masses

Answer 1

The correct option is A Decreases by a factor of $4$

Gravitational force acting on bodies of masses $m_1$and $m_2$ separated by a distance $r$ is given by,

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

When the distance between them doubles, $r^{\prime }=2r$

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

Therefore, the gravitational force decreases by a factor of $4$.