What is the ratio of moment of inertia of a ring to a disc? Given that both have masses in the ratio $2:1$ & radii in the ratio $1:2$ respectively.

Four equal masses, $m$ each are placed at the corners of a square of length $\left(l\right)$ as shown in the figure. The moment of inertia of the system about an axis passing through $A$ and parallel to $DB$ would be :

A wheel of mass $10 \mathrm{kg}$ has moment of inertia equal to $0.1 \mathrm{kg} {\mathrm{m}}^2.$ Then its radius of gyration equals $\underline{ }$

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through $\mathrm{O}$ (the centre of mass) and $\mathrm{O}$' (corner point) is:

A thin uniform rectangular plate of mass $2 \mathrm{kg}$ is placed in $X-Y$ plane as shown in the figure. The moment of inertia about $x$-axis is $I_x=0.2 \mathrm{kg} {\mathrm{m}}^2$ and the moment of inertia about $y$ - axis is $I_y=0.3 \mathrm{kg} {\mathrm{m}}^2$. The radius of gyration of the plate about the axis passing through $O$ and perpendicular to the plane of the plate is

Moment of inertia $\left(\mathrm{M}.\mathrm{I}.\right)$ of four bodies, having same mass and radius, are reported as;

$I_1=\mathrm{M}.\mathrm{I}.$ of thin circular ring about its diameter,

$I_2=\mathrm{M}.\mathrm{I}.$ of circular disc about an axis perpendicular to disc and going through the centre,

$I_3=\mathrm{M}.\mathrm{I}.$ of solid cylinder about its axis and

$I_4=\mathrm{M}.\mathrm{I}.$ of solid sphere about its diameter.

Then:

Three identical spherical shells, each of mass $m$ and radius $r$ are placed as shown in the figure. Consider an axis $X{X}^{\mathit{\prime }}$ which is touching the two shells and passing through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about $X{X}^{\mathit{\prime }}$ axis is: