Question

The gravitational force between two objects is $F$. If masses of both the objects are halved without altering the distance between them, then the gravitational force would become

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

Answer 1

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

Gravitational force is given by
$F=\frac{G{m}_1{m}_2}{r^2}$
where G is the gravitational constant, $m_{1}and{m}_2$ are masses and $r$ is the distance between the two masses.
If the masses are halved, then
$F=\frac{G\frac{m_1}{2}\frac{m_2}{2}}{r^2}$
$F=\frac{1}{4}\frac{G{m}_1{m}_2}{r^2}$
So it becomes one-fourth of the original force.