Find the out the moment of inertia of a ring having uniform mass distribution of mass `M` and radius `R` about an axis which is tangent ot the ring and (`a`) in the plane of the ring (`b`). perpendicular to the plane of the ring.

Explanation

Moment of inertia of a circular ring of mass `M` and radius `R` about the diameter `AB`, Fig.

`I_(AB) = (MR^(2))/(2)`
The given axis is `XY`, tangent to the ring in the plane of ring and parallel to its diameter `AB`. using the theorem of parallel axes,
`I_(XY) = I_(AB) + MR^(2) = (1)/(2)MR^(2) + MR^(2) = (3)/(2)MR^(2)`