A disc of mass $M$ and radius $R$ is rolling with angular speed $\omega $ on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origion $O$ is
$\frac{1}{2}\,M{R^2}\omega $
$M{R^2}\omega $
$\frac{3}{2}\,M{R^2}\omega $
$2M{R^2}\omega $
$A$ uniform rod $AB$ of length $L$ and mass $M$ is lying on a smooth table. $A$ small particle of mass $m$ strike the rod with a velocity $v_0$ at point $C$ a distance $x$ from the centre $O$. The particle comes to rest after collision. The value of $x$, so that point $A$ of the rod remains stationary just after collision, 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
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 ....... $kg$
A uniform solid sphere of mass $m$ and radius $r$ rolls without slipping down a inclined plane, inclined at an angle $45^o$ to the horizontal. Find the magnitude of frictional coefficient at which slipping is absent
A child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u,$ the centre of mass of the system (trolley + child) will move with a speed.