Question

The gravitational force between two objects is $F$. If both of their masses are halved without altering the distance between them, the new gravitational force between them would be:

• A. $2F$
• B. $\frac{F}{2}$
• C. $\frac{F}{4}$
• D. $4F$

Answer 1

The correct option is C $\frac{F}{4}$

The gravitational force, $F$ between two bodies, $m_1$ and $m_2$ seperated by distance $d$ is given by,
$F=\frac{G{m}_1{m}_2}{d^2}$, where G is the gravitational constant.

So, when the masses are halved, the new gravitaional force, $F_{new}$ becomes :
$F_{new}=\frac{G\frac{m_1}{2}\frac{m_2}{2}}{d^2}$
$⟹F_{new}=\frac{G{m}_1{m}_2}{4d^2}$ $\therefore F_{new}=\frac{F}{4}$.