Question

If the distance between two bodies becomes $6$ times of the initial value, the gravitational force between the two bodies becomes:

• A. $\frac{1}{6}$ times
• B. $\frac{1}{36}$ times
• C. $6$ times
• D. $36$ times

Answer 1

The correct option is B $\frac{1}{36}$ times

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 universal constant.
$\therefore F\propto \frac{1}{d^2}$

So, if the distance between two bodies becomes 6 times of the initial value, the gravitational force between them would be $\frac{1}{6^2}$ or $\frac{1}{36}$ times of the initial value.