For a cube of side $a$ and mass $M$,the moment of inertia is minimum about which axis?

The moment of inertia of a thin semicircular disc (mass $= M$ and radius $= R$) about an axis passing through point $O$ and perpendicular to the plane of the disc is given by:

Consider a uniform wire of mass $M$ and length $L$. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre 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

Four particles,each of mass $m$,are placed at the corners of a square of side $l$. The radius of gyration of the system about an axis passing through the center of the square and perpendicular to its plane is:

The radius of gyration of a uniform rod of length $l$ about an axis passing through a point $\frac{l}{4}$ away from the centre of the rod and perpendicular to it is: