$A$ wheel of mass $10 \ kg$ has a moment of inertia of $160 \ kg \ m^2$ about its axis. Its radius of gyration is ...... $m$.

Three thin rods,each of mass $2M$ and length $L$,are placed along the $x, y,$ and $z$ axes,which are mutually perpendicular. One end of each rod is at the origin. The moment of inertia of the system about the $x$-axis is:

The moment of inertia of a cylinder of mass $M$,length $L$,and radius $R$ about an axis passing through its centre and perpendicular to the axis of the cylinder is $I = M \left(\frac{R^2}{4} + \frac{L^2}{12}\right)$. If such a cylinder is to be made for a given mass of material,the ratio $L/R$ for it to have the minimum possible $I$ is

Two spheres of equal masses,one of which is a thin spherical shell and the other a solid sphere,have the same moment of inertia about their respective diameters. The ratio of their radii is

Assertion $(A)$: The moment of inertia of a steel sphere is larger than the moment of inertia of a wooden sphere of the same radius.
Reason $(R)$: Moment of inertia is independent of the mass of the body.
The correct one is:

$A$ flywheel rotates about its axis with a constant angular velocity. If a particle suddenly sticks to its rim,what will happen to its moment of inertia?