Moment of Inertia of a circular wire about an axis nn′ passing through the centre of the circle and perpendicular to the plane of the circle =MR2
As shown in the figure, X-axis and Y-axis lies in the plane of the ring. Then by perpendicular axis theorem IX+IY=IZ ⇒2IX=MR2[. as IX−IY (by symmetry) and .IZ=MR2] ∴IX=