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, as the mass density is uniform, centre of mass is located at their respective geometrical centres.
No, it is not neessary that the centre of mass of a body should lie on the body. For example, in case of a cirular ring, centre of mass is at the centre of the ring, where there is no mass.