JEE Main 2025 — Center of Mass Momentum and Collision Question with Solution

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 $v_{\mathrm{A}}=5\mathrm{m}/\mathrm{s},v_{\mathrm{B}}=2\mathrm{m}/\mathrm{s},v_{\mathrm{C}}=4\mathrm{m}/\mathrm{s}$. If we wait sufficiently long for elastic collision to happen, then $v_{\mathrm{A}}=4\mathrm{m}/\mathrm{s},v_{\mathrm{B}}=2\mathrm{m}/\mathrm{s}$, $v_{\mathrm{C}}=5\mathrm{m}/\mathrm{s}$ 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 :