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What happens to the gravitational force between two objects when the distance between them is: (i) doubled? (ii) halved?
We know gravitational force $F=G\frac{m_1m_2}{r^2}$
Here, $m_1\rightarrow$ mass of first object
$m_2\rightarrow$ mass of the second object
$r\rightarrow$distance between the two object
(i). If the distance between the two objects is doubled, then it becomes $2r$
Then, gravitational force $F'=G\frac{m_1m_2}{(2r)^2}$
$=\frac{1}{4}\times G\frac{m_1m_2}{r^2}$
$=\frac{F}{4}$
Thus, on doubling the distance between the two objects, the
gravitational force becomes one-fourth.
(ii). If the distance between the two objects is halved, it becomes
$\frac{r}{2}$
Then, gravitational force $F'=G\frac{m_1m_2}{(\frac{r}{2})^2}$
$=4\times G\frac{m_1m_2}{r^2}$
$=4F$
Thus, if the distance between the two objects is halved, the
gravitational force becomes four times.