Physics - Gravitation Question with Solution | TestHub

The gravitational potential at the center of a uniform solid sphere is $V_C=-\frac{3GM}{2R}$, and at its surface is $V_S=-\frac{GM}{R}$. The work done by an external agent to move a mass $m$ from the center to the surface is $W=m(V_S-V_C)$. Substituting the values, $W=m(-\frac{GM}{R}-(-\frac{3GM}{2R}))=m(-\frac{GM}{R}+\frac{3GM}{2R})=m(\frac{-2GM+3GM}{2R})=\frac{GMm}{2R}$.