$A$ solid sphere $A$ and a hollow sphere $B$ have the same mass and the same external radius. If their moments of inertia about their diameters are $I_A$ and $I_B$ respectively,then which of the following is true?

Two discs,one of density $7.2 \, g/cm^3$ and the other of density $8.9 \, g/cm^3$,have the same mass and thickness. What is the ratio of their moments of inertia?

$A$ thin uniform rectangular plate of mass $2 \, kg$ is placed in the $xy$-plane as shown in the figure. The moment of inertia about the $x$-axis is $I_{x}=0.2 \, kg \cdot m^{2}$ and the moment of inertia about the $y$-axis is $I_{y}=0.3 \, kg \cdot m^{2}$. The radius of gyration of the plate about the axis passing through $O$ and perpendicular to the plane of the plate is (in $ \, cm$)

The ratio of the radius of gyration of a circular disc about an axis in its plane and tangent to it,to the radius of gyration of a circular ring about an axis in its plane and tangent to it is .........

The figure shows an isosceles triangular plate of mass $M$ and base $L$. The angle at the apex is $90^o$. The apex lies at the origin and the base is parallel to the $X$-axis. The moment of inertia of the plate about the $y$-axis is:

The ratio of radii of gyration of a thin circular ring and a circular disc of same radius about a tangential axis in their own planes is $\sqrt{12}: \sqrt{K}$. The value of $K$ is