A large number of particles are situated at a distance $\mathrm{R}$ from the origin. If particles are uniformly distributed and make a circular boundary around the origin, the centre of mass will lie at the origin.

Whereas, if the particles are not uniformly distributed, then distance can be any value between zero and $\mathrm{R}$

This implies the distance between the centre of mass and the origin is always less than or equal to $\mathrm{R}$