A uniform metre stick of mass $M$ is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial angular acceleration of free end of the stick if the string is cut? (in $rad/sec^2$ )

Two spheres are rolling with same velocity (for their $C. M.$) their ratio of kinetic energy is $2 : 1$ & radius ratio is $2 : 1$, their mass ratio will be :

In the following figure $r_1$ and $r_2$ are $5\,cm$ and $30\,cm$ respectively. If the moment of inertia of the wheel is $1500\,kg\,m^2$ then its angular acceleration will be (Approximately) 

One circular ring and one ciruclar disc, both are having the same mass and radius. the ratio of their moments of inertia about the axis passing through their centres and perpendicular to their planes, will be

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

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