The moment of inertia of a uniform circular disc about its diameter is $I$. What is its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim (in $, I$)?

The moment of inertia of a solid cylinder about its own axis is equal to its moment of inertia about an axis passing through its center of gravity and perpendicular to its length. What is the relationship between its length $L$ and radius $R$?

Consider a uniform horizontal solid cylinder of mass $10 \,kg$ such that its length is $9$ times its radius. Let the radius be $40 \,cm$. Calculate the moment of inertia of the cylinder about a line passing through its edge and perpendicular to its axis.

For which of the following objects can the moment of inertia $NOT$ be found using the perpendicular axis theorem?

The moment of inertia of a thin uniform rod of mass $M$ and length $L$,about an axis perpendicular to the length of the rod and at a distance $L/4$ from one end is:

Seven identical discs are arranged in a planar pattern,so as to touch each other as shown in the figure. Each disc has mass $m$ and radius $R$. What is the moment of inertia of the system of six outer discs about an axis passing through the centre of the central disc and normal to the plane of all discs?