A solid sphere of mass M and radius R lies concentrically inside a spherical shell of mass M and radius 2R. A particle of mass M is placed at a distance 4R from the common centre as shown in the figure. The total potential energy of interaction of the system of masses is

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$- \frac{G M^{2}}{2 R}$

$- \frac{G M^{2}}{4 R}$

$- \frac{G M^{2}}{R}$

$- \frac{G M^{2}}{8 R}$

answer is A.

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Detailed Solution

Total potential energy of the system = interaction energy of them.

$[- \frac{G M M}{4 R} - \frac{G M M}{4 R} - \frac{G M M}{2 R}] = - \frac{G M^{2}}{R}$

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