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.