$A$ uniform rod of mass $M$ and length $L$ has a moment of inertia $I$ about an axis passing through its center and perpendicular to the rod. What will be its moment of inertia about an axis passing through one of its ends and perpendicular to the rod?

$A$ small circular disc of radius $R/3$ is cut from a larger circular disc of radius $R$ and mass $9M$. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through $O$ is:

$A$ thin square plate $ABCD$ has a uniform thickness. What is the moment of inertia about an axis passing through its center and perpendicular to its plane?

What is the moment of inertia of a square sheet of side $l$ and mass per unit area $\mu$ about an axis passing through the centre and perpendicular to its plane?

The moment of inertia of a rod of mass $40 \text{ kg}$ and length $3 \text{ m}$ about an axis $AB$ passing through its end and perpendicular to its length is equal to the moment of inertia of a solid sphere of mass $10 \text{ kg}$ and radius $R$ about an axis parallel to the $AB$ axis, with a separation of $3 \text{ m}$ between the axes, as shown in the figure. The value of $R$ is given as $\sqrt{\frac{\alpha}{2}}$. The value of $\alpha$ 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 $........... \times 10^{-3}\,kg\,m^2$.