The gravitational force between two bodies is 1 N. If distance be…

Question

The gravitational force between two bodies is $1 N.$ If distance between them is doubled, what will be the gravitational force between them?

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Answer

Let $m_1$ and $m_2$ be masses of the given two bodies. If they are $r$ distance apart initially, then the force between them will be,
$F =\frac{ G m _1 m_2}{ r ^2}=1 N\ \ \ \ ......(i)$
When the distance between them is doubled,
$r^{\prime}=2 r$
$\therefore F^{\prime}=\frac{G m_1 m_2}{(2 r)^2}=\frac{G m_1 m_2}{4 r^2}\ \ \ \ \ ......(ii)$
Dividing equation $(ii)$ by equation $(i),$
$\frac{ F ^{\prime}}{ F }=\frac{ Gm _1 m_2}{4 r ^2} \times \frac{ r ^2}{G m_1 m_2}$
$\therefore F ^{\prime}=\frac{ F }{4}=\frac{1}{4}=0.25 N$
The force between two bodies reduces to $0.25 N.$

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