The moment of inertia of a uniform circular disc of radius $R$ and mass $M$ about an axis passing through the edge of the disc and normal to the disc 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 . . . . . . .

$A$ solid sphere of radius $R$ has mass $M$. The moment of inertia of the solid sphere about an axis at a distance $\frac{R}{2}$ from the centre is:

Two rings of the same radius and mass are placed such that their centers coincide and their planes are mutually perpendicular. The moment of inertia of the system about an axis passing through the center and perpendicular to the plane of one of the rings is ...... (where mass $= m$,radius $= r$)

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through which of the following points?

Moment of inertia of a disc about an axis which is tangent and parallel to its plane is $I$. Then the moment of inertia of disc about a tangent,but perpendicular to its plane will be