Two rods,each of mass $m$ and length $l$,are joined at their centers to form a cross. What is the moment of inertia of the cross about an axis passing through their common center and perpendicular to the plane of the rods?

$A$ quarter of a uniform circular disc of radius $R$ is cut off. The mass of the cut-off part is $M$. It rotates about an axis passing through the center of the original disc and perpendicular to the plane of the disc. What will be its moment of inertia about the axis of rotation?

Three identical thin rods each of mass $m$ and length $l$ are placed along $x, y$ and $z$-axes respectively. They are placed such that one end of each rod is at the origin $O$. The moment of inertia of this system about the $z$-axis 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?

$Assertion$ : Radius of gyration of a body is a constant quantity.
$Reason$ : The radius of gyration of a body about an axis of rotation may be defined as the root mean square distance of the particles from the axis of rotation.

We have two spheres,one of which is a hollow shell and the other solid. They have identical masses and moments of inertia about their respective diameters. The ratio of their radii is given by