$A$ flywheel rotates about its axis with a constant angular velocity. If a particle suddenly sticks to its rim,what will happen to its moment of inertia?

$A$ square sheet of edge length $L$ and uniform mass per unit area $\sigma$ is used to form a hollow cylinder. The moment of inertia of this cylinder about its central axis is

$A$ circular disc of radius $10 \ cm$ and thickness $5 \ mm$ has a uniform density of $8 \ g/cc$. Find the moment of inertia of the disc about an axis passing through its center and perpendicular to its plane.

Two rings have their moments of inertia in the ratio $2:1$ and their diameters are in the ratio $2:1$. The ratio of their masses is

Three thin rods,each of mass $M$ and length $L$,are placed along the $X$,$Y$,and $Z$ axes,which are mutually perpendicular. One end of each rod is at the origin. The moment of inertia of the system about the $Z$ axis is:

$A$ thin uniform rectangular plate of mass $2 \, kg$ is placed in the $xy$-plane as shown in the figure. The moment of inertia about the $x$-axis is $I_{x}=0.2 \, kg \cdot m^{2}$ and the moment of inertia about the $y$-axis is $I_{y}=0.3 \, kg \cdot m^{2}$. The radius of gyration of the plate about the axis passing through $O$ and perpendicular to the plane of the plate is (in $ \, cm$)