Potential at center of two concentric shells – Rankers Physics
Topic: Gravitation
Subtopic: Gravitational Potential

Potential at center of two concentric shells

Two concentric shells have mass \(M\) and \(m\) and their radii are \(R\) and \(r\) respectively, where \(R > r\). What is the gravitational potential at their common centre ?
\(-\frac{GM}{R}\)
\(-\frac{GM}{r}\)
\(-G\left[\frac{M}{R} - \frac{m}{r}\right]\)
\(-G\left[\frac{M}{R} + \frac{m}{r}\right]\)

Solution:

The potential at the center of a shell of mass \(M\) and radius \(R\) is \(-\frac{GM}{R}\). By superposition, the total potential at the common center is \(V = -\frac{GM}{R} - \frac{Gm}{r} = -G\left[\frac{M}{R} + \frac{m}{r}\right]\).

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