$A$ disc and a ring both have the same mass and radius. The ratio of the moment of inertia of the disc about its diameter to that of a ring about a tangent in its plane is

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 $L/3$ from one of its ends and perpendicular to the rod is:

$A$ lamina is made by removing a small disc of diameter $2R$ from a bigger disc of uniform mass density and radius $2R$,as shown in the figure. The moment of inertia of this lamina about axes passing through $O$ and $P$ is $I_0$ and $I_P$,respectively. Both these axes are perpendicular to the plane of the lamina. The ratio $\frac{I_P}{I_0}$ to the nearest integer is:

The moment of inertia of a uniform ring of mass $M$ and radius $r$ about a tangent in its own plane is:

$A$ solid sphere of mass $500\,g$ and radius $5\,cm$ is rotated about one of its diameters with an angular speed of $10\,rad\,s^{-1}$. If the moment of inertia of the sphere about its tangent is $x \times 10^{-2}$ times its angular momentum about the diameter,then the value of $x$ will be ..............

$A$ solid sphere of radius $R$ has a moment of inertia $I$ about its geometrical axis. It is melted into a disc of radius $r$ and thickness $t$. If its moment of inertia about the tangential axis (which is perpendicular to the plane of the disc) is also equal to $I$,then the value of $r$ is equal to: