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 is

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$\sqrt{2r}$

$\sqrt{3r}$

2 r

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

answer is B.

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Detailed Solution

$\begin{array}{l} F = \frac{{Gm}_{1} m_{2}}{r^{2}} {If m}_{1} = m_{2} then \Rightarrow F = \frac{Gmm}{r^{2}} \Rightarrow \frac{{Gm}^{2}}{r^{2}} \\ {If m}_{1} = {m.m}_{1} = \frac{1}{2} {m then F}^{1} = \frac{Gm \frac{m}{2}}{{r_{1}}^{2}} \Rightarrow \frac{{Gm}^{2}}{{2r}_{1}^{2}} \\ If F = F^{1} \Rightarrow \frac{{Gm}^{2}}{r^{2}} = \frac{{Gm}^{2}}{{2r}_{1}^{2}} \Rightarrow 2 r_{1}^{2} = r^{2} \Rightarrow r_{1} = \frac{r}{\sqrt{2}} \end{array}$