Give 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 inside the body?
Give 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 inside the body?

All of the structures are symmetrical bodies with a fairly consistent mass density. As a result, the centre of mass for all of the above bodies will be in their geometric centres.

The centre of mass of a body does not always have to be inside it; for example, the centre of mass of a circular ring is at its centre.