In a one-dimensional collision between two identical particles. A and B, B is stationary and A has momentum `p` before impact. During impact, B gives an impulse J to A. Find the coefficient of restitution between A and B?

Options

A. The total momentum of the `A+B` System is `p` before and after impact, and `(p - 1)` during the impact.
B. During the impact A given impulse J to B
C. the coefficient of restituation is `(2J)/(p) - 1`
D. The coefficient of restituation is `(J)/(p) + 1`

Answer

B, C

Explanation

`underset(A)overset(P)overset(rarr)"O" + underset(B)"O" = underset(A)"O" larrJ" " Jrarrunderset(B)"O"`
For `A : P - J = mv_(1)` …(i)
for `B : J = mv_(2)` ….(ii)
`:. e = -((v_(1) - v_(1))/(u_(2) - u_(2))) = -[(J)/(m)- (((P -J)/(m)))/(0 - (P)/(m))] = (2J)/(P) -1`