Two points of a rigid body are moving as shown. The angular velocity of the body is: ?
$\frac{\upsilon }{{2R}}$
$\frac{\upsilon }{R}$
$\frac{{2\upsilon }}{R}$
$\frac{{2\upsilon }}{{3R}}$
A mass $‘m’$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?
When a uniform solid sphere and a disc of the same mass and of the same radius rolls down a rough inclined plane from rest to the same distance, then the ratio of the time taken by them is
$A$ 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 :
A uniform bar of length $'6l'$ and mass $'8m'$ lies on a smooth horizontal table. Two point masses $m$ and $2m$ moving in the same horizontal plane with speed $2v$ and $v$ respectively, strike the bar (as shown in the fig.) and stick to the bar after collision. Total energy (about the centre of mass, $c$ ) will be