Two circular discs of iron have the same thickness. The diameter of disc $A$ is twice that of disc $B$. The moment of inertia of $A$ will be ........ times that of $B$.

Five solid spheres,each of mass $m$ and radius $r$,are arranged as shown in the figure. The axis of rotation $A-A'$ passes through the centers of three spheres. Calculate the moment of inertia of the system about the axis of rotation $A-A'$. (in $m r^2$)

Two rods of equal mass $m$ and length $l$ lie along the $x$-axis and $y$-axis with their centers at the origin. What is the moment of inertia of both about the line $x=y$?

If the diameter of a flywheel is increased by $1\%$,then the percentage increase in its moment of inertia about an axis passing through its center will be ....... $\%$

$A$ 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$)

Four point masses,each of mass $m$,are fixed at the corners of a square of side $\ell$. The square is rotating with angular frequency $\omega$,about an axis passing through one of the corners of the square and parallel to its diagonal,as shown in the figure. The angular momentum of the square about this axis is $.......m\ell^2 \omega$.