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If $M_{e}$ is the mass of earth and $M_{m}$ is the mass of moon ( $M_{e} = 81 M_{m}$ ). The potential energy of an object of mass $m$ situated at a distance $R$ from the centre of earth and $r$ from the centre of moon, will be :-

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$- G m M_{m} (\frac{R}{81} + r) \frac{1}{R^{2}}$

$- G m M_{e} (\frac{81}{r} + \frac{1}{R})$

$- G m M_{m} (\frac{81}{R} + \frac{1}{r})$

$G m M_{m} (\frac{81}{R} - \frac{1}{r})$

answer is C.

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Detailed Solution

$U = - \frac{G M_{e} m}{R} - \frac{G M_{m} m}{r} = - \frac{G (81 M_{m}) m}{R} - \frac{G M_{m} m}{r} = - G m M_{m} (\frac{81}{R} + \frac{1}{r})$

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