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In a one-dimensional collision between two identical particles A and B, B is initially at rest and A has momentum p just before impact. During the impact, B receives an impulse J from A. Which statement is correct?

1. The total momentum of the A-plus-B system is p before and after impact, but (p - J) during the impact.
2. During the impact, A gives B an impulse of magnitude J.
3. The coefficient of restitution is (2J/p) - 1.
4. Both (B) and (C) are correct.

Correct answer: Both (B) and (C) are correct.

Solution

Impulse from A to B equals J (statement B correct). With equal masses, after impact B's momentum = J and A's momentum = p - J. Approach speed ~ p/m, separation speed ~ (J - (p-J))/m = (2J - p)/m, so e = (2J - p)/p = 2J/p - 1 (statement C correct). Hence both B and C are correct. Total momentum is conserved (always p), so the 'during impact' statement is wrong.

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