Two solid spheres ($A$ and $B$) are made of metals having densities $\rho_A$ and $\rho_B$ respectively. If their masses are equal,then the ratio of their moments of inertia $(\frac{I_B}{I_A})$ about their respective diameters 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 perpendicular to the square and passing through its centre is

The ratio of the masses of two circular rings is $1:2$ and the ratio of their diameters is $2:1$. The ratio of their moments of inertia is:

The moment of inertia $(M.I.)$ of four bodies,having the same mass $M$ and radius $R$,are reported as follows:
$I_{1} = M.I.$ of a thin circular ring about its diameter.
$I_{2} = M.I.$ of a circular disc about an axis perpendicular to the disc and passing through the centre.
$I_{3} = M.I.$ of a solid cylinder about its axis.
$I_{4} = M.I.$ of a solid sphere about its diameter.
Then:

Moment of inertia of a solid sphere about its diameter is $I$. It is then casted into $27$ small spheres of same diameter. The moment of inertia of each new sphere is

If a person sitting on a rotating stool with his hands outstretched, suddenly lowers his hands, then his