Question

If the distance between two bodies becomes 6 times more than the usual, the gravitational force between the two bodies would become the usual.

• A. $\frac{1}{12}$ times
• B. $\frac{1}{36}$ times
• C. $36$ times
• D. $6$ times

Answer 1

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

The gravitational force, $\text{F}$ between two bodies, ${\text{m}}_1$ and ${\text{m}}_2$ seperated by distance $\text{d}$ is given by, $\text{F}=\frac{\text{G}{\text{m}}_1{\text{m}}_2}{{\text{d}}^2}$, where $\text{G}$ is the universal gravitational constant.
$⟹\text{F}\propto \frac{1}{{\text{d}}^2}$
So, if the distance between the two bodies becomes 6 times the usual, the force of gravity between them would be $\frac{1}{6^2}$ = $\frac{1}{36}$ times the usual.