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 $R$?

As shown in the figure,two thin coplanar circular discs $A$ and $B$ each of mass $M$ and radius $r$ are attached to form a rigid body. The moment of inertia of this system about an axis perpendicular to the plane of disc $B$ and passing through its centre is (in $Mr^2$)

The moment of inertia of a circular ring about an axis perpendicular to its plane and passing through its center is $200 \, gm \cdot cm^2$. The moment of inertia about its diameter is ....... $gm \cdot cm^2$.

$A$ sphere of radius $R$ is cut from a larger solid sphere of radius $2R$ as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the $Y$-axis is

Let $I$ be the moment of inertia of a uniform square plate about an axis $AB$ that passes through its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\theta$ with $AB$. The moment of inertia of the plate about the axis $CD$ is then equal to:

Three identical thin rods,each of length $l$ and mass $M$,are joined together to form the letter $H$. What is the moment of inertia of the system about one of the vertical sides of the $H$?