The moment of inertia of a semicircular ring of radius $R$ and mass $M$ about an axis passing through point $A$ (one end of the ring) and perpendicular to the plane of the paper is:

$A$ thin circular disc is in the $xy$ plane as shown in the figure. The ratio of its moment of inertia about $z$ and $z'$ axes will be

From a uniform circular thin disc of mass $9 M$ and radius $R$,a small disc of radius $\frac{R}{3}$ is removed. The centre of the small disc is at a distance $\frac{2 R}{3}$ from the centre of the original disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the original disc of radius $R$ is

The moment of inertia of a sphere about its diameter is $40 \ kg \cdot m^2$. Find the moment of inertia about any tangent.

Three identical spheres,each of mass $M$ and radius $R$,are placed as shown in the figure. Consider an axis $XX'$ which passes through the diameter of the top sphere and is tangent to the two bottom spheres. The moment of inertia of the system consisting of these three spheres about the $XX'$ axis is:

Consider a uniform square plate of side '$a$' and mass '$m$'. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is