Gravitational Potential at Common Centre – Rankers Physics
Topic: Gravitation
Subtopic: Gravitational Potential

Gravitational Potential at Common Centre

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 gravitational potential inside any spherical shell is constant and equals the potential at its surface. Therefore, the total potential at the common centre is the sum of the potentials: \(V = -\frac{GM}{R} - \frac{Gm}{r} = -G\left[\frac{M}{R} + \frac{m}{r}\right]\).

Leave a Reply

Your email address will not be published. Required fields are marked *