In the given figure linear acceleration of solid cylinder of mass $m_2$ is $a_2$. Then angular acceleration $\alpha_2$ is (given that there is no slipping).
$\frac{a_2}{R}$
$\frac{a_2 + g}{R}$
$\frac{2(a_2 + g)}{R}$
$\frac{2(g - a_2)}{R}$
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
Three particles are connected by massless rods lying along the $y-$ axis. If the system rotates about the $x-$ axis with an angular speed of $2\, rad/s$, the $M.I.$ of the system is ......... $kg-m^2$
Two points of a rigid body are moving as shown. The angular velocity of the body 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
A loop rolls down on an inclined plane. The fraction of its total kinetic energy that is associated with the rotational motion is