The masses of the earth and moon are M and M/n respectively. Their centres are separated by a distance 2r. The minimum speed with which a particle of mass m should be projected from a point midway the two centres so as to escape to infinity is

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$\sqrt{\frac{2 (GMn)}{(n + 1) r}}$

$\sqrt{\frac{2 GM (n + 1)}{nr}}$

$\sqrt{\frac{GM (n + 1)}{2 nr}}$

$\sqrt{\frac{GM (n + 1)}{nr}}$

answer is B.

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Detailed Solution

Apply law of conservation of Energy

$\frac{- GMm}{r} - \frac{G \frac{M}{n} m}{r} + \frac{1}{2} {mV}^{2} = 0$

$\Rightarrow \frac{V^{2}}{2} = \frac{GM}{r} (1 + \frac{1}{n}) \Rightarrow V = \sqrt{\frac{2 GM (n + 1)}{nr}}$

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