Question.
How does the force of gravitation between two objects change when the distance between them is reduced to half ?
How does the force of gravitation between two objects change when the distance between them is reduced to half ?
Solution:
When all other variables remain constant, the force of gravitation is inversely proportional to the square of distance between the two objects.
$F \propto \frac{1}{r^{2}} \Rightarrow \frac{F^{\prime}}{F}=\frac{r^{2}}{\left(\frac{r}{2}\right)^{2}}=\frac{4 r^{2}}{r^{2}}=4$
$\therefore$ The force of gravitation increases 4 times.
When all other variables remain constant, the force of gravitation is inversely proportional to the square of distance between the two objects.
$F \propto \frac{1}{r^{2}} \Rightarrow \frac{F^{\prime}}{F}=\frac{r^{2}}{\left(\frac{r}{2}\right)^{2}}=\frac{4 r^{2}}{r^{2}}=4$
$\therefore$ The force of gravitation increases 4 times.