JEE Main 2025 Jan 29 Shift 2, Physics Q11: Newton's Laws Of Motion

JEE Main2025Jan 29, Shift 2Physics

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 :

A
Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
B
(A) is true but (R) is false
C
Both (A) and (R) are true and (R) is the correct explanation of (A).
D
(A) is false but (R) is true

Solution

(R) is a standard result for one-dimensional elastic collisions of equal masses: the two participants swap velocities.

Apply this rule to the chain. With ordering and initial velocities $v_{A} = 5, v_{B} = 2, v_{C} = 4$ (all rightward), A catches B first because $v_{A} > v_{B}$ .

Collision 1 (A with B): A and B swap velocities. New velocities: $v_{A} = 2, v_{B} = 5, v_{C} = 4$ .

Now B (moving at $5$ ) catches C (moving at $4$ ).

Collision 2 (B with C): they swap. Final: $v_{A} = 2, v_{B} = 4, v_{C} = 5$ .

Comparing with the claimed final values $v_{A} = 4, v_{B} = 2, v_{C} = 5$ : A and B do not match, so Assertion is false. Reason is true.

$∴$ Option (4) is correct.

Concept behind this question

Newton's Laws Of MotionNotes, formulas and examples →

Practice more Physics

Concept-wise practice with instant solutions on Fundamenthol.

Start practicing →

JEE Main 2025 Jan 29 Shift 2, Physics Q11: Newton's Laws Of Motion

Concept behind this question

More previous year questions on Newton's Laws Of Motion

Practice more Physics