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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:

Asked in JEE Main 29th Jan 2nd Shift 2025 · Velocity exchange and mass ratios

• (1) (A) is false but (R) is true
• (2) Both (A) and (R) are true and (R) is the correct explanation of (A)
• (3) Both (A) and (R) are true but (R) is not the correct explanation of (A)
• (4) (A) is true but (R) is false

Step-by-step solution

Why the other options are wrong

• (2) Comes from accepting the velocity set in the assertion without tracing the two swaps; A ends at 2 m/s, not 4.
• (3) Comes from accepting the assertion's velocities and doubting the exchange rule, which is exact for equal masses.
• (4) Comes from rejecting the exchange rule; it is what makes the final set 2,4,5.

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