$A$ solid cylinder has mass $M$,length $L$,and radius $R$. What is the moment of inertia of this cylinder about one of its generators?

$A$ circular plate of mass $M$ and radius $R$ has its density varying as $\rho(r) = \rho_0 r$,where $\rho_0$ is a constant and $r$ is the distance from its center. The moment of inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is $I = aMR^2$. The value of the coefficient $a$ is:

$A$ circular hole of diameter $R$ is cut from a disc of mass $M$ and radius $R$; the circumference of the cut passes through the centre of the disc. The moment of inertia of the remaining portion of the disc about an axis perpendicular to the disc and passing through its centre is

Three solid spheres each of mass $M$ and radius $R$ are arranged as shown in the figure. The moment of inertia of the system about $YY'$ will be

The moment of inertia of a thin square plate $ABCD$ of uniform thickness about an axis passing through the centre $O$ and perpendicular to the plane of the plate is given by which of the following expressions? Here,$I_1, I_2, I_3,$ and $I_4$ are the moments of inertia about axes $1, 2, 3,$ and $4$ respectively,which lie in the plane of the plate as shown in the figure.

Three rings each of mass $M$ and radius $R$ are arranged as shown in the figure. The moment of inertia of the system about the axis $YY'$ is: