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
$\frac{{2m{v^2}}}{5}$
$\frac{{m{v^2}}}{5}$
$\frac{{3m{v^2}}}{5}$
$m{v^2}$
A sphere of diameter $r$ is cut from a sphere of radius $r$ such that the centre of mass of the remaining mass be at maximum distance from original centre; then the distance is
A thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega $. Two objects, each of mass $m$, are attached gently to the opposite ends of a diameter of the ring. The ring rotates now with an angular velocity
In a gravity free space, a man of mass $M$ standing at a height $h$ above the floor, throws a ball of mass $m$ straight down with a speed $u$ . When the ball reaches the floor, the distance of the man above the floor will be
Two rotating bodies $A$ and $B$ of masses $m$ and $2\,m$ with moments of innertia $I_A$ and $I_B\,(I_B > I_A)$ have equal kinetic energy of rotation. If $L_A$ and $L_B$ be their angular momentum respectively, then
A cylinder of mass $M$ and radius $r$ is mounted on a frictionless axle over a well. A rope of negligible mass is wrapped around the solid cylinder and a bucket of mass $m$ is suspended from the rope. The linear acceleration of the bucket will be