$A$ circular disc $A$ of radius $r$ is made from an iron plate of thickness $t$ and another circular disc $B$ of radius $4r$ is made from an iron plate of thickness $t/4$. The relation between the moments of inertia $I_A$ and $I_B$ is:

$A$ rod of linear mass density $\lambda$ and length $L$ is bent to form a ring of radius $R$. The moment of inertia of the ring about any of its diameters is:

Point masses of $1, 2, 3,$ and $4 \ kg$ are placed at $(0, 0, 0), (2, 0, 0), (0, 3, 0),$ and $(-2, -2, 0)$ respectively. What is the moment of inertia of this system about the $x$-axis in $kg-m^2$?

The moment of inertia of a solid sphere about its diameter is $I$. It is then recast into $27$ small spheres of the same diameter. The moment of inertia of each small sphere about its diameter 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$)

The moment of inertia of a thin circular lamina of mass $1\,kg$ and diameter $0.2\,m$ rotating about one of its diameters is