A ball of mass M moving with a velocity V collides head on elastically with another of same mass but moving with a velocity v in the opposite direction. After collision,

the velocities are exchanged between the two balls

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both the balls come to rest

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both of them move at right angles to the original line of motion

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one ball comes to rest and another ball travels back with velocity 2V

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Solution

The correct option is B the velocities are exchanged between the two balls
Using conservation of linear momentum we have:
$M_{1} u_{1} - M_{2} u_{2} = - M_{1} v_{1} + M_{2} v_{2}$

$M V - M u_{2} = - M v + M v_{2}$
$V - u_{2} = - v + v_{2}$ .............(i)
and as for a perfect elastic collision we have $e = 1$ , thus we get
$v_{2} + v = u_{2} + V$ .................(ii)
Using these two equations we get:
$u_{2} = v$ and $v_{2} = V$
Thus, the velocities are exchanged between the two balls.

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