$A$ wire of mass $M$ and length $L$ is bent in the form of a circular ring. The moment of inertia of the ring about its axis is

The radius of gyration of a body depends upon

The linear mass density of a thin rod $AB$ of length $L$ varies from $A$ to $B$ as $\lambda(x) = \lambda_{0}(1 + \frac{x}{L})$,where $x$ is the distance from $A$. If $M$ is the mass of the rod,then its moment of inertia about an axis passing through $A$ and perpendicular to the rod is $......ML^{2}$.

Two circular loops $A$ and $B$ of radii $R$ and $NR$ respectively are made from a uniform wire. The moment of inertia of $B$ about its axis is $3$ times that of $A$ about its axis. The value of $N$ is:

$A$ solid spherical ball of density $\rho_{1}$ and a hollow spherical ball of density $\rho_{2}$ have the same outer radius $R$ and the same mass $M$. What is the ratio of the moment of inertia of the hollow sphere to that of the solid sphere about an axis passing through their centers?

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