A solid sphere rolls without slipping and presses a spring of spring constant $'k'$ as shown in figure. Then, the compression in the spring will be :-
$v\sqrt {\frac{{2m}}{{3k}}} $
$v\sqrt {\frac{{5k}}{{7m}}} $
$v\sqrt {\frac{{2m}}{{5k}}} $
$v\sqrt {\frac{{7m}}{{5k}}} $
Two point masses of $0.3\ kg$ and $0.7\ kg$ are fixed at the ends of a rod of length $1.4\ m$ and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of
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 wheel of moment of inertia $10\ kg-m^2$ is rotating at $10$ rotations per minute. The work done in increasing its speed to $5$ times its initial value, will be.......... $J$
Two discs of moment of inertia $I_1$ and $I_2$ and angular speeds ${\omega _1}\,{\rm{and }}{\omega _2}$ are rotating along collinear axes passing through their centre of mass and perpendicular to their plane. If the two are made to rotate together along the same axis the rotational $KE$ of system will be
A flywheel is making $\frac{3000}{\pi}$ revolutions per minute about its axis. If the moment of inertia of the flywheel about that axis is $400\, kgm^2$, its rotational kinetic energy is