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The distance between two bodies is decreased by a factor of 3. How is the magnitude of gravitational force between them affected ?

Force

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Answer

As we know,

F = G m1m2r2\dfrac{\text{m}1\text{m}2}{\text{r}^2}

If separation between two bodies is decreased by a factor of 3 then,

F = G m1m2(r3)2\dfrac{\text{m}1\text{m}2}{{(\dfrac{\text{r}}{3}})^2} = 9G m1m2r2\dfrac{\text{m}1\text{m}2}{\text{r}^2}

Therefore, the gravitational force will be increased by a factor of 9.

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