The moment of inertia of a rod (length $l$,mass $m$) about an axis perpendicular to the length of the rod and passing through a point equidistant from its midpoint and one end is:

$A$ uniform square plate of side $a$ and mass $m$ is given. The moment of inertia of this plate about an axis perpendicular to the plate and passing through one of its corners is .......

$A$ 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

Two hollow spheres each of mass $M$ and radius $\frac{R}{2}$ are connected with a massless rod of length $2R$ as shown in the figure. What will be the moment of inertia of the system about an axis $yy'$ passing through the center of one of the spheres and perpendicular to the rod?

Calculate the moment of inertia of an annular disc about an axis tangent to the outer circle and lying in the plane of the disc. The mass of the disc is $M$,the inner radius is $R_1$,and the outer radius is $R_2$.

The moment of inertia of a uniform thin rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $\frac{L}{4}$ from one of its ends and perpendicular to the rod is: