In a head on collision between two identical particles A and B moving on a horizontal surface, B is stationary and A has momentum `P_(0)` before impact. Due to the impact, A recrieves an impulse I. Then coefficient of restitution between the two is :

Options

A. `(2I)/P_(0)-1`
B. `(2I)/P_(0)+1`
C. `(I)/P_(0)+1`
D. `(I)/P_(0)-1`

Answer

A

Explanation

Ans. (1)

Impulse `=DeltaP`
So, For `B`, `I=mv_(2)......(i)`
and For `A`, `-I=mv_(1)-P_(0)....(ii)`
`rArre=(v_(2)-v_(1))/(-(0-v_(0)))=(mv_(2)-mv_(1))/(mv_(0))=(I-(P_(0)-I))/(P_(0))=(2I-P_(0))/(P_(0))`
`e=(2I)/(P_(0))-1`