The gravitational force between two equal masses at a distance r is F. When one of the masses becomes half, the distance at which it should be kept so that the gravitational force remains same

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\sqrt{3} r

\sqrt{2} r

\frac{r}{\sqrt{2}}

answer is B.

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Detailed Solution

Given that for

m_{1} = m = m_{2} r = r

We know $F = \frac{{Gm}_{1} m_{2}}{r^{2}}$

$F_{1} = \frac{{Gm}^{2}}{r^{2}}$

Now $m_{1} = m, m_{2} = \frac{m}{2} r^{|} = ?$

To get $F_{2} = F_{1}$

$\Rightarrow F_{2} = \frac{G m_{1} m_{2}}{{(r^{|})}^{2}} \Rightarrow \frac{G \frac{m \times m}{2}}{{(r^{|})}^{2}}$

$\frac{{Gm}^{2}}{r^{2}} = \frac{{Gm}^{2}}{2 {(r^{|})}^{2}}$

$\Rightarrow {(r^{|})}^{2} = \frac{r^{2}}{2} \Rightarrow r^{|} = \frac{r}{\sqrt{2}}$

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