What will be the gravitational potential (V) at a point between two bodies of masses m and M, kept at a distance d apart, where the gravitational field due to them is zero.

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$V = - \frac{GM}{d}$

$V = - \frac{G}{d} (m + M)$

$V = - \frac{Gm}{d}$

$V = \frac{G}{d} (\sqrt{m} + \sqrt{M})^{2}$

answer is D.

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Detailed Solution

$the gravitational field at a distance x from m where it is zero is \frac{Gm}{x^{2}} = \frac{GM}{{(d - x)}^{2}} solving for x we get x = \frac{d \sqrt{m}}{\sqrt{m} + \sqrt{M}} potential at that point - \frac{Gm}{x} - \frac{GM}{d - x} V = \frac{G}{d} (\sqrt{m} + \sqrt{M})^{2}$

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