A particle of mass $m$ is placed at the center of a thin spherical shell of mass $M$ and radius $R$. The gravitational potential at a distance $r$ from the center, where $r<R$, is given by:

Solution

1. The gravitational potential due to a shell of mass $M$ and radius $R$ at any point inside is constant.
2. The potential inside is equal to the potential at the surface, which is $V=-GM/R$.
3. The mass $m$ at the center does not contribute to the potential at distance $r$.
4. Hence the answer is (A).