$A$ wheel (rim) of mass $6 \ kg$ and radius $40 \ cm$ is rotating at a rate of $300 \ rpm$. Its moment of inertia is ....... $kg \cdot m^2$.

$A$ solid hemisphere and a hemispherical shell are joined as shown. Both of them have a mass of $m/2$ individually. Find the moment of inertia about the axis $AB$.

The three rods $A$,$B$,and $C$ shown in the figure have the same length $L$ and the same mass $M$. If the system rotates such that rod $B$ acts as the axis of rotation,what will be the moment of inertia of the system?

$A$ 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?

The ratio of the radii of gyration of a circular disc to that of a circular ring,each of same mass and radius,around their respective axes is

$A$ 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$)