When two bodies collide elastically,then

$A$ body of mass $M$ moves with velocity $v$ and collides elastically with another body of mass $m$ $(M >> m)$ at rest. Then,the velocity of the body of mass $m$ is:

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

An object of mass $m_{1}$ collides with another object of mass $m_{2}$,which is at rest. After the collision,the objects move with equal speeds in opposite directions. The ratio of the masses $m_{2} : m_{1}$ is

$A$ neutron travelling with a velocity $v$ and kinetic energy $E$ collides perfectly elastically head-on with the nucleus of an atom of mass number $A$ at rest. The fraction of total energy retained by the neutron is

$A$ sphere of mass $M$ moving with velocity $u$ undergoes a perfectly elastic head-on collision with another sphere of mass $m$ at rest. After the collision,their velocities are $V$ and $v$ respectively. Find the value of $v$.