The moment of inertia of a uniform circular ring,having a mass $M$ and a radius $R$,about an axis tangential to the ring and perpendicular to its plane,is

$A$ system of five solid spheres, each of mass $m$ and radius $r$, is rotating about an axis $AA'$. The moment of inertia of the system about the axis of rotation $AA'$ is: (in $mr^2$)

Moment of inertia of a body about two perpendicular axes $X$ and $Y$ in the plane of the lamina are $20 \text{ kg m}^2$ and $25 \text{ kg m}^2$ respectively. Its moment of inertia about an axis perpendicular to the plane of the lamina and passing through the point of intersection of $X$ and $Y$ axes is:

$A$ solid sphere and a disc of same mass $M$ and radius $R$ are kept such that their curved surfaces are in contact and their centers lie along the same horizontal line. The moment of inertia of the two-body system about an axis passing through their point of contact and perpendicular to the plane of the disc is

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.

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