Two identical balls $A$ and $B$ are released from the positions shown in figure. They collide elastically on horizontal portion $MN$ . The ratio of the heights attained by $A$ and $B$ after collision will be : (neglect friction)

A proton of mass $m$ collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of $90^o$ with respect to each other. The mass of unknown particle is

A sphere collides with another sphere of identical mass. After collision, the two spheres move. The collision is inelastic. Then the angle between the directions of the two spheres is

A body of mass $M$ moves with velocity $v$ and collides elastically with a another body of mass $m$ ($M>>m$) at rest then the velocity of body of mass $m$ is

$A$ flexible chain of length $2m$ and mass $1kg$ initially held in vertical position such that its lower end just touches a horizontal surface, is released from rest at time $t = 0$. Assuming that any part of chain which strikes the plane immediately comes to rest and that the portion of chain lying on horizontal surface does not from any heap, the height of its centre of mass above surface at any instant $t = 1/\sqrt 5$ befor it completely comes to rest) is ................ $\mathrm{m}$

A sphere $P$ of mass $m$ and moving with velocity $v$ undergoes an oblique and  perfectly elastic collision with an identical sphere $Q$ initially at rest. The angle $\theta$ between the velocities of the spheres after the collision shall be .............. $^o$