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

The moment of inertia of a thin rod about an axis passing through its midpoint and perpendicular to the rod is $2400 \,g \,cm^2$. The length of the $400 \,g$ rod is nearly: (in $\,cm$)

Four point masses,each of value $m$,are placed at the corners of a square $ABCD$ of side $l$. The moment of inertia of this system about an axis passing through $A$ and parallel to $BD$ is

$A$ person is sitting on a rotating table with their arms outstretched. If they suddenly pull their arms inward,then:

From a uniform wire, two circular loops are made: $(i)$ $P$ of radius $r$ and (ii) $Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its centre and perpendicular to its plane is $8$ times that of $P$ about a similar axis, the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$). (in $\sqrt{2}$)

The radius of gyration of a disc of mass $50 \, g$ and radius $2.5 \, cm$ about an axis passing through its center of gravity and perpendicular to its plane is ....... $cm$.