Question

How does the force of gravitation between two objects change when the distance between them is reduced to half?

Answer 1

According to the universal law of gravitation, gravitational force ($F$) acting between two objects is inversely proportional to the square of the distance ($r$) between them, i.e.,

$𝐹∝ \frac{1 }{𝑟^2 }$
If distance r becomes $\frac{r}2$, then the gravitational force will be proportional to
$\frac1{ (\frac𝑟{2})^2}$ = $\frac4{𝑟^2}$

Hence, if the distance is reduced to half, then the gravitational force becomes four times larger than the previous value.