An iron circular disc $X$ has radius $R$ and thickness $t$. Another iron circular disc $Y$ has radius $4R$ and thickness $t/4$. The relationship between the moments of inertia $I_X$ and $I_Y$ of these two discs is .......

Two rings of same mass $m$ and radius $R$ are placed with their planes perpendicular to each other and centres at a common point. The radius of gyration of the system about an axis passing through the centre and perpendicular to the plane of one ring is ............

$A$ solid sphere $A$ is rotating about an axis $PQ$. If the radius of the sphere is $5 \, cm$ and the distance of its center from the axis $PQ$ is $10 \, cm$,then its radius of gyration about $PQ$ will be $\sqrt{x} \, cm$. The value of $x$ is $................$.

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 $.......m\ell^2 \omega$.

What is the radius of gyration of a circular disc of radius $R$ about an axis passing through its center and perpendicular to its plane?

The moment of inertia depends on: