The first ball of mass `m` moving with the velocity `upsilon` collides head on with the second ball of mass `m` at rest. If the coefficient of restitution is `e`, then the ratio of the velocities of the first and the second ball after the collision is

Options

A. `(1-e)/(1+e)`
B. `(1+e)/(1-e)`
C. `(1+e)/(2)`
D. `(1-e)/(2)`

Answer

A

Explanation

Here, `m_(1)=m_(2)=m, u_(1)=u, u_(2)=0`. Let `upsilon_(1), upsilon_(2)` be their velocities after collision.
According to principle of conservation of linear momentum.
`m u +0=m(upsilon_(1)+upsilon_(2))` or `upsilon_(1)+upsilon_(2)=u ….(1)`
By definition, `e=(upsilon_(2)-upsilon_(1))/(u-0)`
or `upsilon_(2)-upsilon_(1)= e u .....(ii)`
Add `(i)` and `(ii)``upsilon_(2)=(u(1+e))/(2)`
Subtract `(ii)` from `(i)` `upsilon_(1)=((1-e)u)/(2) :. (upsilon_(1))/(upsilon_(2))=(1-e)/(1+e)`