$A$ thin metal wire of length $L$ and mass $M$ is bent to form a semicircular ring as shown. The moment of inertia about the axis $XX^1$ passing through its ends is:

The radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass is:

If a solid sphere and a solid cylinder of the same radius and density rotate about their own axes,which one will have a greater moment of inertia? (Assume $L = R$)

$A$ quarter of a uniform circular disc of radius $R$ is cut off. The mass of the cut-off part is $M$. It rotates about an axis passing through the center of the original disc and perpendicular to the plane of the disc. What will be its moment of inertia about the axis of rotation?

Three identical rods,each of length $l$ and mass $M$,are joined to form a rigid equilateral triangle. Its radius of gyration about an axis passing through a corner and perpendicular to the plane of the triangle is

$A$ solid spherical ball of density $\rho_{1}$ and a hollow spherical ball of density $\rho_{2}$ have the same outer radius $R$ and the same mass $M$. What is the ratio of the moment of inertia of the hollow sphere to that of the solid sphere about an axis passing through their centers?