According to the theorem of parallel axes $I = I_g + Md^2$,the graph between $I$ and $d$ will be

The $X$ and $Z$ axes are mutually perpendicular in the plane of a disc,and the $Y$ axis is perpendicular to the plane of the disc. If the moments of inertia of the object about the $X$ and $Y$ axes are $30 \ kg \ m^2$ and $40 \ kg \ m^2$ respectively,then the moment of inertia about the $Z$ axis will be ....... $kg \ m^2$.

The moment of inertia of a thin square plate $ABCD$ of uniform thickness about an axis passing through the centre $O$ and perpendicular to the plane of the plate is given by which of the following expressions? Here,$I_1, I_2, I_3,$ and $I_4$ are the moments of inertia about axes $1, 2, 3,$ and $4$ respectively,which lie in the plane of the plate as shown in the figure.

Four identical thin rods,each of mass $M$ and length $l$,form a square frame. The moment of inertia of this frame about an axis passing through the centre of the square and perpendicular to its plane is

Three spheres,each of mass $m$ and radius $r$,are placed as shown in the figure. Consider an axis $YY^1$,which is tangent to two spheres (labeled $2$ and $3$) and passes through the diameter of the third sphere (labeled $1$). The moment of inertia of the system consisting of these three spheres about the $YY^1$ axis is:

The radius of gyration $K$ of a hollow sphere of mass $M$ and radius $R$ about an axis $XY$ is equal to $R$. The distance of that axis from the center of the sphere is $h$. The value of $h$ is