A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega $. Its centre of mass rises to a maximum height of:
$\frac{1}{3}\frac{{{l^2}{\omega ^2}}}{g}$
$\frac{1}{6}\frac{{l\omega }}{g}$
$\frac{1}{2}\frac{{{l^2}{\omega ^2}}}{g}$
$\frac{1}{6}\frac{{{l^2}{\omega ^2}}}{g}$
The given figure shows a disc of mass $M$ and radius $R$ lying in the $x-y$ plane with its centre on $x$ axis at a distance a from the origin. then the moment of inertia of the disc about the $x-$ axis is
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 solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane making an angle $\theta $ with the horizontal. then its acceleration is
A force $\vec F$ acts on a particle having position vector $\vec r$ (with respect to origin). It produces a torque $\vec \tau $ about origin, choose the correct option
A solid sphere is rolling on a frictionless surface, shown in figure with a translational velocity $v\,\,m/s.$ If it is to climb the inclined surface then $v$ should be