A ball of mass m moving with a constant velocity strikes against a ball of same mass at rest. If `e=` coefficient of restitution, then what will the the ratio of the velocities of the two balls after collision?

Options

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

Answer

A

Explanation

In this problem , `u_(1) =u,u_(2) =0 , m_(1)=m_(2)=m`
`:. " Using "m_(1)u_(1) +m_(2)u_(2) =m_(1)v_(1) +m_(2)v_(2) ` we get
`:. u +0 = mv_(1) +mv_(2)`
`:. u = v_(1)+v_(2) " "...(1)`
The coefficient of restitution as
`e=(v_(2)-v_(1))/(u_(1)-u_(2))=(v_(2)-v_(1))/(u-0):. eu=v_(2)-v_(1)" "...(2)`
`:.` Adding (1) and (2) , we get `u+eu=2v_(2)`

`:.v_(2)=(u(1+e))/(2)" "...(3)`
and on subtracting (2) from (1) we get,
`u - eu = 2v_(1) :. v_(1) = (u(1-e))/(2) " "...(4)`
`:.` From (3) and (4) , `(V_(1))/(V_(2)) = (1-e)/(1+e) " " (5)`