Find the moment of inertia of a solid cylinder of mass $M$ and radius $R$ about a line parallel to the axis of the cylinder and on the surface of the cylinder.

Find the moment of inertia of a plate cut in the shape of a right-angled triangle of mass $M$ and sides $AC = BC = a$,about an axis perpendicular to the plane of the plate and passing through the midpoint of the side $AB$.

The moment of inertia of a disc, of mass $M$ and radius $R$, about an axis which is a tangent and parallel to its diameter is

Two identical solid spheres each of mass $2\,kg$ and radii $10\,cm$ are fixed at the ends of a light rod. The separation between the centres of the spheres is $40\,cm$. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is $........... \times 10^{-3}\,kg\,m^2$.

Three thin metal rods,each of mass $M$ and length $L$,are welded to form an equilateral triangle. The moment of inertia of the composite structure about an axis passing through the centre of mass of the structure and perpendicular to its plane 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