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 ?

Explanation

(i) Centre of mass of a sphere lieson its geometric centre, it is inside the body.
(ii) Centre of mass of a cylinder lies on the mid point of axis or on geometric centre, it is inside the cylinder.
(iii) Centre of mass of a ring lies on the centre of ring and its outside the material of ring.
(iv) Centre of mass of a cube lies on the 8 cross-section point of diagonals or on the geometric cube.
The centre of mass of a body need not necessarily lie within it. For example, ring, hollow cylinder, hollow sphere and hollow cube etc. their central of mass lies outside the body, while for circular disc, square disc, solid sphere, rectangular disc, cone etc. all have centre of mass inside the body.