The ratio of the radius of gyration of a circular disc to that of a circular ring,each of the same mass and radius,about their respective central axes is:

$5$ particles,each of mass $2 \ kg$,are attached to the rim of a circular disc of radius $0.1 \ m$ and negligible mass. The moment of inertia of this system about an axis passing through the center and perpendicular to its plane is ........... $kg \cdot m^{2}$.

Two identical thin rods of mass $M \ kg$ and length $L \ m$ are connected as shown in the figure. The moment of inertia of the combined rod system about an axis passing through point $P$ and perpendicular to the plane of the rods is $\frac{x}{12} M L^2 \ kg \ m^2$. The value of $x$ is . . . . . . .

$A$ thin wire of length $\ell$ and mass $m$ is bent in the form of a semicircle as shown. Its moment of inertia about an axis joining its free ends will be ...........

Three particles,each of mass $m \; g$,are situated at the vertices of an equilateral triangle $ABC$ of side $l \; cm$ (as shown in the figure). The moment of inertia of the system about a line $AX$ perpendicular to $AB$ and in the plane of $ABC$ in $g \cdot cm^2$ units will be:

Four particles,each of mass $1 \ kg$,are placed at the four corners of a square of side $2 \ m$. The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its vertices is . . . . . . $kg \ m^2$.