Gravitaional potential at a point

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Question

Two point masses m and 4m are at separation r. P is a point where gravitational field is zero. Then gravitational potential at point P is

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Solution

$\frac{G . m}{x^{2}} = \frac{G .4 m}{{(r - x)}^{2}} \Rightarrow r - x = 2 x \Rightarrow x = \frac{r}{3}$
$∴ V_{P} = - \frac{G . m}{\frac{r}{3}} - \frac{G .4 m}{\frac{2 r}{3}} = \frac{- 9 G m}{r}$

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