Question

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

Answer 1

Step 1: Given Data

Let the initial distance be $r$.

Final distance $=\frac{r}{2}$

Let the mass of the two objects be $m_1$ and $m_2$.

Universal gravitation constant $=G$

Step 2: Formula used

According to Newton's law of Gravitation $F=G\frac{m_1{m}_2}{r^2}$

Step 3: Change is Gravitational Force

According to Newton's law of Gravitation,

Initial force $F=G\frac{m_1{m}_2}{r^2}$

Therefore, the final force $F\text{'}=G\frac{m_1{m}_2}{{\left({\displaystyle \raisebox{1ex}{$r$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right)}^2}$

$=4G\frac{m_1{m}_2}{r^2}$

$=4F$

Hence, when the distance between the objects is reduced to half, the gravitational force increases four times.