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:

Ring is symmetric with respect to all of its diameters, therefore the moment of inertia of ring about all the diameters is same. Let I_d be the moment of inertia of ring about its diameter. According to the theorem of perpendicular axis,

(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 centre and perpendicular to plane is I = MR². Let I_t be the moment of inertia of ring about tangent parallel to diameter. Using theorem of parallel axis,