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:

Three point masses,each of mass $m$,are placed at the corners of an equilateral triangle of side $\ell$. The moment of inertia of the system about an axis passing through one of the vertices and parallel to the side joining the other two vertices is:

Two circular rings $A$ and $B$ of radii $nR$ and $R$ are made from the same wire. The moment of inertia of $A$ about an axis passing through the centre and perpendicular to the plane of $A$ is $64$ times that of the ring $B$. The value of $n$ is:

$A$ solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively $(k_{\text{sph}} : k_{\text{cyl}})$ is $2 : \sqrt{x}$,then the value of $x$ is .............

The moment of inertia of a meter scale of mass $0.6 \ kg$ about an axis perpendicular to the scale and located at the $20 \ cm$ position on the scale in $kg-m^2$ is: (Breadth of the scale is negligible)

$A$ semi-circular disc has mass $M$ and radius $r$. The moment of inertia about an axis passing through its center and perpendicular to the plane of the disc is: