What is the moment of inertia of a thin circular disc about its diameter? ($M$ is the mass and $R$ is the radius of the disc.)

The ratio of the radii of gyration of a circular disc to that of a circular ring,each of same mass and radius,around their respective axes is

Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is $K_c$. Radius of gyration of the same disc about a diameter of the disc is $K_d$. The ratio $K_d : K_c$ is

Let $M$ and $L$ be the mass and length of a thin uniform rod, respectively. In the first case, the axis of rotation passes through the centre and is perpendicular to the length of the rod. In the second case, the axis of rotation passes through one end and is perpendicular to the length of the rod. The ratio of the radius of gyration in the first case to the second case is:

$A$ solid hemisphere and a hemispherical shell are joined as shown. Both of them have a mass of $m/2$ individually. Find the moment of inertia about the axis $AB$.

Consider a uniform wire of mass $M$ and length $L$. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is: