The moment of inertia of a semicircular plate of radius $R$ and mass $M$ about an axis $AA'$ in its plane passing through its centre is given by:

The moment of inertia of a solid sphere about its diameter is $I$. It is then recast into $27$ small spheres of the same diameter. The moment of inertia of each small sphere about its diameter is:

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is

$A$ uniform thin bar of mass $6 \,kg$ and length $2.4 \,m$ is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the hexagon is ...... $\times 10^{-1} \,kg \cdot m^2$.

The moment of inertia $I$ of a solid sphere having fixed volume depends upon its volume $V$ as

Five masses,each of $2\, kg$,are placed on a horizontal circular disc that can rotate about a vertical axis passing through its center. All masses are equidistant from the axis at a distance of $10\, cm$. Calculate the moment of inertia of the whole system in $gm-cm^2$. (Assume the disc has negligible mass.)