Question

Force of gravitation between two objects become ____times of its initial value, when the distance between them is reduced to one-fourth of its initial value?

• A. $2$
• B. $4$
• C. $8$
• D. $16$

Answer 1

The correct option is D $16$

Let $M_1$ and $M_2$ be the mass of two objects and $R$ be the distance between them.
Using universal law of gravitation,
$F=\frac{G{M}_1{M}_2}{R^2}$
where $G$ is the universal gravitational constant.

New distance is $R^{\prime }=R/4$.
Let the new force be $F^{\prime }$.
$F^{\prime }=\frac{G{M}_1{M}_2}{R^{\prime 2}}$
$F^{\prime }=\frac{G{M}_1{M}_2}{(R/4{)}^2}$
$F^{\prime }=16\frac{G{M}_1{M}_2}{R^2}$
$F^{\prime }=16F$