The moment of inertia of a uniform horizontal solid cylinder of mass $M$ about an axis passing through its edge and perpendicular to the axis of the cylinder,when its length is $6$ times its radius $R$,is:

The moment of inertia of a triangular plate $ABC$ of mass $M$ and side $BC = a,$ about an axis passing through $A$ and perpendicular to the plane of the plate is :-

Consider a thin uniform square sheet made of a rigid material. If its side is $a$,mass is $m$,and the moment of inertia about one of its diagonals is $I$,then:

The moment of inertia of a semicircular disc of mass $M$ and radius $R$ about the shown axis is:

If $I$ is the moment of inertia of a thin circular disc about an axis passing through the tangent of the disc and in the plane of the disc,what is the moment of inertia of the same circular disc about an axis perpendicular to the plane and passing through its centre?

$A$ lamina is made by removing a small disc of diameter $2R$ from a bigger disc of uniform mass density and radius $2R$,as shown in the figure. The moment of inertia of this lamina about axes passing through $O$ and $P$ is $I_0$ and $I_P$,respectively. Both these axes are perpendicular to the plane of the lamina. The ratio $\frac{I_P}{I_0}$ to the nearest integer is: