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 ........ $m.$

A circular disc is rolling on a horizontal plane. Its total kinetic energy is $300\,J$ . ....... $J$ is its translational $K.E$

In an experiment with a beam balance an unknown mass $m$ is balanced by two known masses of $16\,kg$ and $4\,kg$ as shown in figure. The value of the unknown mass $m$ is ....... $kg$

Moment of inertia of a uniform annular disc of internal radius $r$ and external radius $R$ and mass $M$ about an axis through its centre and perpendicular to its plane is

$A$ bob of mass $m$ is attached to a string whose other end is tied to a light vertical rod as shown in figure. The bob is swinging in horizontal plane with constant angular speed $\omega$. The vertical rod is supported on a block of mass $M$ which is placed on a rough surface. What is minimum friction coefficient between ground and block for which block does not slip ?

A $T-$ shaped object of uniform thickness and same material with dimensions shown in the figure, is lying on a smooth floor. A force $\vec F$ is applied at the point $P$ parallel to $AB,$ such that the object has only the translation motion without rotation. Find the location of $P$ with respect to $C$