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:

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 . . . . . . .

The moment of inertia of a uniform circular disc about its diameter is $I$. What is its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim (in $, I$)?

$A$ 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?

The moment of inertia of a circular ring of mass $M$ and diameter $r$ about a tangential axis lying in the plane of the ring is

The moment of inertia of a solid sphere about its diameter is $I$. Two such spheres are arranged as shown in the figure. The moment of inertia of the system about axis $AB$ will be