The centre of mass of a uniform circular ring or a disc lies at its geometric centre.
The centre of mass of a disc of uniform mass and radius r, when a circular portion of radius β has been removed from it such that centre of the hole is at distance η from the centre of disc is :
Mass of a ring is non-uniformly distributed around its geometric centre. If
R is radius of the ring, then
a. centre of mass does not coincide with geometric centre
b. Position centre of mass from the geometric centre will be x (0<x<R)
c. centre of mass will be nearer to the greater mass distribution
d. centre of mass may lie outside the periphery