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.

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Updated on: 10-Oct-2022

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