Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2016 / S29 / 3 / b / Solution

Build a solid uniform sphere from thin shells: $dC=(2/3)r^2(4\pi \rho r^{2}dr)$. Integration gives $C=8\pi \rho R^5/15$, while $M=4\pi \rho R^3/3$. Hence $\boxed{C=2M{R}^2/5}$. This is a spherical uniform-density model; planetary flattening modifies the exact relation.