The moment of inertia of a uniform semicircular wire of mass $M$ and radius $r$ about a line perpendicular to the plane of the wire through the centre is:

A thin rod of length $L$ and mass $M$ is bent at the middle point $O$ as shown in the figure. Consider an axis passing through two middle the point $O$ and perpendicular to the plane of the bent rod. Then the moment of inertia about this axis is

The moment of inertia of a uniform disc about $O{O}^{\text{'}}$ is

Three rings each of mass $m$ and radius $r$ are so placed that they touch each other. The radius of gyration of the system about the axis as shown in the figure is

Let $I$ be the moment of inertia of a uniform square plate about an axis $AB$ that passes through its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\mathrm{\theta }$ with $AB$ as shown in figure. The moment of inertia of the plate about the axis $CD$ is then equal to