If a solid sphere of mass $5 \, kg$ and a disc of mass $4 \, kg$ have the same radius $R$,then the ratio of the moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent is $\frac{x}{7}$. The value of $x$ is $.........$

The $X$ and $Z$ axes are mutually perpendicular in the plane of a disc,and the $Y$ axis is perpendicular to the plane of the disc. If the moments of inertia of the object about the $X$ and $Y$ axes are $30 \ kg \ m^2$ and $40 \ kg \ m^2$ respectively,then the moment of inertia about the $Z$ axis will be ....... $kg \ m^2$.

$A$ circular hole of diameter $R$ is cut from a disc of mass $M$ and radius $R$; the circumference of the cut passes through the centre of the disc. The moment of inertia of the remaining portion of the disc about an axis perpendicular to the disc and passing through its centre is

What is the moment of inertia of a rod of mass $M$ and length $l$ about an axis perpendicular to it passing through one end?

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 $= r$)

If the moment of inertia of a uniform solid cylinder about the axis of the cylinder is $\frac{1}{n}$ times its moment of inertia about an axis passing through its midpoint and perpendicular to its length,then the ratio of the length and radius of the cylinder is