The moment of inertia of a semicircular ring about an axis passing through the center and perpendicular to the plane of the ring is $\frac{1}{x} MR^2$,where $R$ is the radius and $M$ is the mass of the semicircular ring. The value of $x$ will be $...........$

Two spheres $A$ and $B$,each of mass $5 \ kg$,are attached to the ends of a light rod of length $1 \ m$. Treating the spheres as point masses,find the ratio of the moment of inertia of the system about an axis passing through $A$ to that about an axis passing through the center of the rod,both axes being perpendicular to the rod.

Moment of Inertia $(M.I.)$ of four bodies having same mass $M$ and radius $2R$ are as follows:
$I_{1} =$ $M.I.$ of solid sphere about its diameter
$I_{2} =$ $M.I.$ of solid cylinder about its axis
$I_{3} =$ $M.I.$ of solid circular disc about its diameter
$I_{4} =$ $M.I.$ of thin circular ring about its diameter
If $2(I_{2} + I_{3}) + I_{4} = x I_{1}$,then the value of $x$ will be...

Calculate the moment of inertia of the system shown in the figure about the axis of rotation $XX'$.

If the radius of a solid sphere is $35\,cm,$ calculate the radius of gyration when the axis is along a tangent.

$A$ solid sphere and a solid cylinder have the same mass and same radius. The ratio of the moment of inertia of the solid sphere about its diameter and the moment of inertia of the solid cylinder about its axis is