$A$ body of mass $m$ and radius of gyration $K$ has an angular momentum $L$. Then its angular velocity is

In a rectangle $ABCD$ where $BC = 2AB$,the moment of inertia will be minimum about which axis?

Four particles each of mass $M$ are placed at the corners of a square of side $L$. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

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

$A$ solid sphere of radius $r = 5 \text{ cm}$ is rotating about an axis at a distance $d = 10 \text{ cm}$ from its center, as shown in the figure. If the radius of gyration about that axis is $\sqrt{x} \text{ cm}$, then the value of $x$ is:

$A$ light rod of length $l$ has two masses $m_1$ and $m_2$ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is