Question

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 ?

Answer 1

Locations for each body

• (i) Sphere (solid, uniform): At the geometric centre of the sphere.
• (ii) Cylinder (solid, uniform): At the midpoint of its axis, i.e. the geometric centre of the cylinder.
• (iii) Ring (uniform circular ring): At the centre of the ring, i.e. at the centre of the circle formed by the ring.
• (iv) Cube (solid, uniform): At the point where the body diagonals intersect, i.e. the geometric centre of the cube.

Does the centre of mass always lie inside the body?

No. The centre of mass of a body does not necessarily lie inside the material of the body. For example, for a uniform ring, hollow sphere, or hollow cylinder, the centre of mass is at the geometric centre, which is in empty space (outside the material).