Question

How much does the force of gravitation between two objects increase when the distance between them is reduced to one-fourth of the initial value?

• A. 2 times
• B. 4 times
• C. 8 times
• D. 16 times

Answer 1

The correct option is D

16 times

Let two masses $M_1$ and $M_2$ be separated by a distance of $R$.

The gravitational force between them is $F=\frac{G{M}_1{M}_2}{R^2}$

$R$ is reduced to ‘$\frac{R}{4}$’, the force of attraction between is

$F_1=\frac{G{M}_1{M}_2}{({\frac{R}{4})}^2}$

$⟹F_1=16\frac{G{M}_1{M}_2}{R^2}=16F$

So, the gravitational force increses by 16 times the initial value.