Four identical point masses (each of mass $m$) are placed on the circumference of a disc. The disc has mass $M$ and radius $R$. What will be the moment of inertia about an axis passing through the center $O$ and perpendicular to the plane of the disc?

Four particles of masses $5 \ kg, 2 \ kg, 3 \ kg$,and $4 \ kg$ are placed at $(0, 0, 0), (2, 0, 0), (0, 3, 0)$,and $(-2, -2, 0)$ respectively. The moments of inertia about the $x$-axis,$y$-axis,and $z$-axis respectively are:

From a uniform wire,two circular loops are made: $(i)\ P$ of radius $r$ and $(ii)\ Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its center and perpendicular to its plane is $8$ times that of $P$ about a similar axis,the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$).

The ratio of masses and radii of two circular rings are $1 : 2$ and $2 : 1$ respectively. What is the ratio of their moments of inertia about their central axes?

Two solid spheres ($A$ and $B$) are made of metals of different densities $\rho_A$ and $\rho_B$ respectively. If their masses are equal,the ratio of their moments of inertia $(I_B / I_A)$ about their respective diameter is

Calculate the moment of inertia of the system shown in the figure about the axis of rotation $XX'$.