Question

the moment of inertia of a disc about an axis perpendicular to the plane of the disc passing through its com is Io. it is folded along a diameter so that is one half becomes perpendicular to another half. calculate its moment of inertia about its diameter

Answer 1

Using perpendicular axis theorem we can write the moment of inertia along any diameter will be $\frac{I_0}{2}$. Now if you fold the disc along any diameter, each half will have same moment of inertia which is equal to the moment of inertia of half of the unfolded disc. So total moment of inertia is will be $\frac{I_0}{2}$