$A$ 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:

$A$ thin wire of length $\ell$ and mass $m$ is bent in the form of a semicircle as shown. Its moment of inertia about an axis joining its free ends will be ...........

From a uniform wire, two circular loops are made: $(i)$ $P$ of radius $r$ and (ii) $Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its centre and perpendicular to its plane is $8$ times that of $P$ about a similar axis, the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$). (in $\sqrt{2}$)

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

Let $M$ and $L$ be the mass and length of a thin uniform rod, respectively. In the first case, the axis of rotation passes through the centre and is perpendicular to the length of the rod. In the second case, the axis of rotation passes through one end and is perpendicular to the length of the rod. The ratio of the radius of gyration in the first case to the second case is:

Let the moment of inertia of a hollow cylinder of length $30\, cm$ (inner radius $r = 10\, cm$ and outer radius $R = 20\, cm$),about its axis be $I$. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also $I$,is ......... $cm$.