If moment of inertia of ring about an axis passing through centre and perpendicular to the plane of ring is I then find the moment of inertia about:
(i) diameter
(ii) tangent parallel to diameter using theorem of parallel or perpendicular axis.
(i) Moment of inertia of ring about diameter:
The moment of Inertia of ring about all the diameters is the same because the ring is symmetric w.r.t.
Let Id be the moment of inertia of ring about its diameter.
According to the theorem of perpendicular axis,
Id + Id = Ia = I 
(ii) Moment of infertia of ring about tangent parallel to diameter:
Let M be the mass and R be the radius of ring.
Then, moment of inertia about axis passing through the centre and perpendicular to plane is I = MR2.
Let It be the moment of inertia of ring about tangent parallel to diameter.
Using the theorem of parallel axis,
