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 / c / Solution

A point mass at the rotation center has zero perpendicular distance to the axis, so $\boxed{C=\int r_{\perp }^{2}dm=0}$. More generally, moving a fixed mass inward lowers its moment even if its total gravitational monopole and outer radius remain fixed.