Given the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie on the body ?

Explanation

In all the four cases, the centre of mass lies at the geometrical centre of the body. This is because the mass density is uniform in all the four cases. The centre of mass may lie outside the body, as in case of a ring, a hollow cylinder, a hollow cube, etc. In these bodies centre of mass is at their centres, where there is no mass.