$A$ 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:

Find the moment of inertia of a thin,massless rod about an axis passing through its centre of mass,where a pair of masses is suspended at both ends of this rod.

$A$ long slender rod is welded to a thin circular disc of diameter $0.5 \ m$ at a point on its circumference. The rod is in the same plane as that of the disc and forms a tangent to the disc. The radius of gyration of the disc about the rod (in $m$) is

Radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass is

The moment of inertia of a solid disc rotating about its diameter is $2.5$ times higher than the moment of inertia of a ring rotating in a similar way. The moment of inertia of a solid sphere which has the same radius as the disc and is rotating in a similar way,is $n$ times higher than the moment of inertia of the given ring. Here,$n=$ . . . . . . . Consider all the bodies have equal masses.

Two rings have their moments of inertia in the ratio $4 : 1$ and their diameters are in the ratio $4 : 1$. The ratio of their masses is