Question

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

Answer 1

Here, `m_(1)=m_(2)=m,u_(1)=u, u_(2)=0`
Let `upsilon_(1)` and `upsilon_(2)` be their respective velocities after collision.
As `m_(1)u_(2)+m_(2)u_(2)=m_(1)upsilon_(1)+m_(2)upsilon_(2)`
`:. m u+0=m(upsilon_(1)+upsilon_(2)) ` or `u=upsilon_(1)+upsilon_(2)` ...(i)
Again, by definition, `e=(upsilon_(2)-upsilon_(1))/(u-0)`
`:. upsilon_(2)-upsilon_(1)=ue`
Solving (i) and (ii), we get
`upsilon_(2)=((1+e)u)/(2)`
`upsilon_(1)=((1-e)u)/(2) :. (upsilon_(1))/(upsilon_(2))=(1=e)/(1+e)`