If a body completes one revolution in $\pi $ $sec$ then the moment of inertia would be

Four point masses are fastened to the corners of $a$ frame of negligible mass lying in the $xy$ plane. Let $w$ be the angular speed of rotation. Then

The $M.I.$ of a body about the given axis is $1.2\,kg \times m^2$ and initially the body is at rest. In order to produce a rotational kinetic energy of $1500\,joule$ an angular acceleration of $25\,rad/sec^2$ must be applied about that axis for a duration of ........ $\sec$.

As shown in the figure, a bob of mass $\mathrm{m}$ is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius $\mathrm{r}$ and mass $m$. When released from rest the bob starts falling vertically. When it has covered a distance of $h$. the angular speed of the wheel will be

A flywheel of moment of inertia $0.32\ kg-m^2$ is rotated steadily at $120\,rad/\sec $ by a $50\,W$ electric motor. The kinetic energy of the flywheel is.......... $J$

Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the bottom of the inclined plane of the ring to that of the cylinder is $\frac{\sqrt{x}}{2}$. Then, the value of $x$ is .... .