A disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in figure. At any instant, for the lower most point of the disc -

A wheel of mass $10\,kg$ has a moment of inertia of $160\,kg-m^2$ about its own axis. The radius of gyration is ........ $m.$

Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when speed of $A$ is $v$ and speed of $B$ is $2v$, speed of center of mass of the system is

A thin wire of length $l$ and uniform linear mass density of $\rho $ is bent into a circular loop with centre $O$ and radius $r$ as shown in the figure. The moment of inertia of the loop about the axis $XX'$ is

We have two spheres one of which is hollow and the other solid. They have identical masses and moment of inertia about their respectively diameters. The ratio of their radius is given by

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