The gravitational force between two objects is F. How will the force change when the distance between them is reduced to one-fourth the original separation?

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Solution

According to the Universal law of gravitation,
$F = \frac{G m_{1} m_{2}}{r^{2}}$
Inititally,

$F = \frac{G m_{1} m_{2}}{r^{2}}$
Finally,

$F^{'} = \frac{G m_{1} m_{2}}{(\frac{r}{4})^{2}}$
$= \frac{G m_{1} m_{2}}{r^{2}} \times 16$
$\Rightarrow F^{'} = 16 F$
Thus the gravitational force between two objects increases by 16 times.

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