$A$ semi-circular disc has mass $M$ and radius $r$. The moment of inertia about an axis passing through its center and perpendicular to the plane of the disc is:

Two half rings are joined as shown in the figure. Each half ring has a radius $R$ and mass $M$. The moment of inertia of the system about the axis $XX'$ is

$A$ circular disc $X$ of radius $R$ is made from an iron plate of thickness $t$,and another disc $Y$ of radius $4R$ is made from an iron plate of thickness $\frac{t}{4}$. Then the relation between the moment of inertia $I_x$ and $I_y$ is

Three thin rods,each of mass $2M$ 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 $x$-axis is:

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?

The moment of inertia of a sphere of mass $M$ and radius $R$ is $I.$ If $M$ is kept constant and a graph is plotted between $I$ and $R,$ then its form would be: