What is gravitational potential energy of system consisting of two concentric spherical shells of mass, m, and 4 m and radii R and 2 R.

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

$- \frac{13 G m^{2}}{2 R}$

$\frac{- 9 G m^{2}}{2 R}$

$- \frac{5 G m^{2}}{2 R}$

answer is D.

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Detailed Solution

$\begin{array}{l} \begin{array}{l} U_{s y s} = U_{self 1}, + U_{self 2}, + U_{interaction} \\ = - \frac{G m^{2}}{2 R} - \frac{1}{2} \frac{G {(4 m)}^{2}}{2 R} - \frac{G (m (4 m))}{2 R} \end{array} \\ = - \frac{13 G m^{2}}{2 R} \end{array}$

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