Question

Find the moment of inertia of a uniform disc of mass M and radius R about a diameter.

Answer 1

Consider x &y two mutually perpendicular diameters of the ring.
$I_x+I_y=I_z$
$I_x=I_y$ (due to symmetry)
$I_z=\frac{M{R}^2}{2}$
$I_x=I_y=\frac{M{R}^2}{4}$