The moment of inertia of a ring of mass $m = 3 \ gm$ and radius $r = 1 \ cm$ about an axis passing through its edge and parallel to its natural axis is:

State the theorem of perpendicular axes and the theorem of parallel axes.

The moment of inertia of a rectangular plate of mass $M$,length $l$,and breadth $b$ about an axis perpendicular to its plane and passing through its center 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 $........... \times 10^{-3}\,kg\,m^2$.

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 $AB$.

For the given uniform square lamina $ABCD$,whose centre is $O$,which of the following relations is correct?