Four particles of mass $m$ each are placed at the four corners of a square of side length $\ell$. The radius of gyration of the system about an axis passing through its center and perpendicular to the plane of the square is .........

The radius of gyration of a circular disc of radius $R$ and mass $m$ rotating about its diameter as an axis is:

$A$ thin wire of length $l$ and mass $m$ is bent in the form of a semicircle. The moment of inertia about an axis perpendicular to its plane and passing through the end of the wire is .............

$A$ thin metal rod of mass $M$ and length $L$ is cut into $4$ equal parts by cutting it perpendicular to its length. If the moment of inertia of the rod about an axis passing through its centre and perpendicular to its axis is $I$,then what is the moment of inertia of each part about a similar axis?

The moment of inertia of a semicircular ring about an axis passing through the center and perpendicular to the plane of the ring is $\frac{1}{x} MR^2$,where $R$ is the radius and $M$ is the mass of the semicircular ring. The value of $x$ will be $...........$

The ratio of radii of gyration of a thin circular ring and a circular disc of same radius about a tangential axis in their own planes is $\sqrt{12}: \sqrt{K}$. The value of $K$ is