$A$ circular disc of mass $9M$ and radius $R$ has a smaller disc of radius $R/3$ cut from it. Calculate the moment of inertia of the remaining portion about an axis passing through the center of the original disc and perpendicular to its plane. (in $MR^2$)

The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through its midpoint and perpendicular to its length is $I_0$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

$A$ circular disc $D_1$ of mass $M$ and radius $R$ has two identical discs $D_2$ and $D_3$ of the same mass $M$ and radius $R$ attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis $OO'$,passing through the centre of $D_1$ as shown in the figure,will be:

Two rings of the same radius and mass are placed such that their centers coincide and their planes are mutually perpendicular. The moment of inertia of the system about an axis passing through the center and perpendicular to the plane of one of the rings is ...... (where mass $= m$,radius $= r$)

$(a)$ Find the moment of inertia of a sphere about a tangent to the sphere,given the moment of inertia of the sphere about any of its diameters to be $2 M R^{2} / 5,$ where $M$ is the mass of the sphere and $R$ is the radius of the sphere.
$(b)$ Given the moment of inertia of a disc of mass $M$ and radius $R$ about any of its diameters to be $M R^{2} / 4,$ find its moment of inertia about an axis normal to the disc and passing through a point on its edge.

Find the moment of inertia of the ring shown in the figure about the axis $AB$.