(2010 Pre)
Solution:
The gravitational potential inside a shell is constant, $V_{\text{shell}} = -\frac{GM}{a}$. For particle, $V_{\text{particle}} = -\frac{GM}{a/2} = -\frac{2GM}{a}$. Total potential is $-\frac{3GM}{a}$.
A particle of mass $M$ is situated at the center of a spherical shell of same mass and radius $a$. The gravitational potential at a point situated at $\frac{a}{2}$ distance from the center, will be:
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