Each spherical shell has a radius $R$ and mass $M$. They are connected by a light massless rod. Calculate the moment of inertia about the axis $xx'$.

The moment of inertia of a circular disc of radius $2 \,m$ and mass $1 \,kg$ about an axis passing through the centre of mass but perpendicular to the plane of the disc is $2 \,kg \,m^{2}$. Its moment of inertia about an axis parallel to this axis but passing through the edge of the disc is (see the given figure).

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 $H$?

$A$ 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

Moment of inertia of a disc about its own axis is $I$. Its moment of inertia about a tangential axis in its plane is

What is the moment of inertia of a thin rod of length $L$ and mass $M$ about an axis perpendicular to the rod and passing through a point at a distance of $L/3$ from one of its ends?