The moment of inertia of a uniform disc of mass $M$ and radius $R$ about an axis passing through its edge and perpendicular to the disc is ..........

From a circular disc of radius $R$ and mass $9M$,a small disc of radius $\frac{R}{3}$ is removed. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through $O$ is:

Three thin metal rods,each of mass $M$ and length $L$,are welded to form an equilateral triangle. The moment of inertia of the composite structure about an axis passing through the centre of mass of the structure and perpendicular to its plane is

Consider a uniform square plate of mass $m$ and side length $a$. What is the moment of inertia of this plate about an axis passing through one of its vertices and perpendicular to its plane?

Each spherical shell has a radius $R$ and mass $M$. They are connected by a light massless rod. Calculate the moment of inertia about the axis $xx'$.

The moment of inertia of a disc about an axis passing through its centre and perpendicular to its plane is $I$. What is the ratio of the moment of inertia about a parallel axis tangential to its rim to the moment of inertia about a parallel axis passing through a point midway between the centre and the rim (in $:1$)?