Physics Class 11 Chapter 7 System of Particles & Rotational Motion | Page 21

We can apply Perpendicular axis theorem here on x axis & y axis and get I’, moment of inertia in z axis.
Iz = Ix + Iy, now as because of symmetry Ix & Iy are same so Iz = I’ = 2I = Mr 2 / 2
Now we can apply parallel axis theorem to find I’’. I’’ = I’ + MR 2 = 3 / 2( MR 2)