The ratio of radii of gyration of a circular ring and a circular disc of the same mass and radius,about an axis passing through their centres and perpendicular to their planes is

From a circular ring of mass $M$ and radius $R$,an arc corresponding to a $90^{\circ}$ sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is $K$ times $MR^{2}$. Then the value of $K$ is

$A$ thin metal wire of length $L$ and mass $M$ is bent to form a semicircular ring as shown. The moment of inertia about the axis $XX^1$ passing through its ends 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

The radius of gyration of a disc of mass $100\,g$ and radius $5\,cm$,about an axis passing through its centre of gravity and perpendicular to the plane,is ....... $cm$.

$A$ thin uniform rod of length $L$ and mass $M$ is bent at the middle point $O$ at an angle of $45^{\circ}$ as shown in the figure. The moment of inertia of the system about an axis passing through $O$ and perpendicular to the plane of the bent rod is: