A body A moving with momentum P collides one-dimensionally with another stationary body B of same mass. During impact, A gives impulse J to B. Then which of the following is/are correct ?
(a) The total momentum of A and B is P before and after impact and (P - J) during the impact.
(b) During the impact, B gives impulse of magnitude J to A.
(c ) The coefficient of restitution is `[(2J)/(P) - 1]`
(d) The coefficient of restitution is `[(2J)/(P) + 1]`

Explanation

According to law of conservation of linear momentum,
`m_(1)u_(1)+m_(2)u_(2)=m_(1)v_(1)+m_(2)v_(2)`
i.e., `m u+m(0)=mv_(1)+mv_(2)`
`rArr P-P_(1)=P_(2)` where `P_(2)=J`, given
`therefore` Coefficient of restitution,
`e=(v_(2)-v_(1))/(u)=(mv_(2)-mv_(1))/(m u)=(P_(2)-P_(1))/(P)`
`= (P_(2)-(P-P_(2)))/(P)=(2P_(2)-P_(1))/(P)`
`therefore = (2J-P)/(P)=(2J)/(P)=1`