Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A):
Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities v_A=5 m / s, v_B=2 m / s, v_C=4 m / s. If we wait sufficiently long for elastic collision to happen, then v_A=4 m / s, v_B=2 m / s, v_C=5 m / s will be the final velocities.
Reason (R): In an elastic collision between identical masses, two objects exchange their velocities.
In the light of the above statements, choose the correct answer from the options given below:

Solution

Physics sir · 4 steps

Follow the collisions one at a time, swapping velocities each time, until no ball is catching the one ahead.

1. Check the reason. For two equal masses in a head-on elastic collision, momentum and kinetic energy conservation give v₁' = v₂ and v₂' = v₁. The two balls swap velocities, so (R) is true.
2. Who hits whom. All three move to the right. A at 5 m/s catches B at 2 m/s. B is slower than C, so B and C cannot collide at the start.

   Stage	v_A (m/s)	v_B (m/s)	v_C (m/s)
   Start	5	2	4
   A hits B, they swap	2	5	4
   B now catches C, they swap	2	4	5

3. No more collisions. Now 2 < 4 < 5: each ball is slower than the one ahead of it, so no ball catches another. The final velocities are v_A = 2, v_B = 4, v_C = 5 m/s, not 4, 2, 5 as the assertion claims.
4. So. (A) is false and (R) is true, which is option (c). The assertion's set cannot even be final, since A at 4 would still catch B at 2.

The idea to keep. In a row of equal masses colliding elastically, swap velocities pair by pair until the speeds increase from back to front. That order is the only possible final state.

Answer from the NTA final answer key. Solution by PrepWiser.