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JEE MAIN - Physics (2025 - 29th January Evening Shift - No. 20)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): JEE Main 2025 (Online) 29th January Evening Shift Physics - Center of Mass and Collision Question 4 English 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:

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

Explanation

We know that two bodies of the same mass exchange their velocities after an elastic head-on collision.

Given, initially,

JEE Main 2025 (Online) 29th January Evening Shift Physics - Center of Mass and Collision Question 4 English Explanation

Here, $${V_{AB}} = {v_A} - {v_B} = 5 - 2 = 3\,m/s$$

$${V_{CB}} = {v_C} - {v_B} = 4 - 2 = 2\,m/s$$

first A will collide with B and the velocities will be exchanged.

i.e. now, V$_A$ = 2 m/s and V$_B$ = 5 m/s and V$_C$ = 4 m/s

As $V_B > V_C$

So, B will collide and exchange the velocities with C.

So, $V_B=4$ m/s. and $V_C=5$ m/s.

Hence, finally,

$$\eqalign{ & {V_A} = 2\,m/s \cr & {V_B} = 4\,m/s \cr & {V_C} = 5\,m/s \cr} $$

So, A is false but R is true.

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