JEE Physics 2025 Question with Solution

Given: Three identical spheres move in one dimension with initial velocities $v_A = 5 \, \text{m/s}$, $v_B = 2 \, \text{m/s}$ and $v_C = 4 \, \text{m/s}$.

Find: Whether the assertion and reason are true, and whether the reason correctly explains the assertion.

For a one-dimensional elastic collision between identical masses, the two colliding objects exchange their velocities.

From the solution working:

$$v_A = 5 \, \text{m/s}, \quad v_B = 2 \, \text{m/s}, \quad v_C = 4 \, \text{m/s}$$

After the collisions, the velocities become

$$v_A' = 2 \, \text{m/s}, \quad v_B' = 4 \, \text{m/s}, \quad v_C' = 5 \, \text{m/s}$$

The assertion claims the final velocities are

$$v_A = 4 \, \text{m/s}, \quad v_B = 2 \, \text{m/s}, \quad v_C = 5 \, \text{m/s}$$

These do not match the worked final velocities shown in the solution. Hence, the assertion is false.

The reason, "In an elastic collision between identical masses, two objects exchange their velocities," is true.

Therefore, the correct option is D: (A) is false but (R) is true.

Given: Identical masses undergoing one-dimensional elastic collisions.

Find: The final set of velocities after sufficient time.

Since the spheres have equal masses, each elastic collision causes the two colliding spheres to exchange velocities.

Initially, sphere A with $5 \, \text{m/s}$ catches sphere B with $2 \, \text{m/s}$, so after their collision the velocities exchange.

Then the sphere carrying velocity $5 \, \text{m/s}$ continues and subsequent exchanges finally produce the set reported in the solution:

$$(2, 4, 5) \, \text{m/s}$$

for $A, B, C$ respectively.

Hence the assertion's stated final set $(4, 2, 5) \, \text{m/s}$ is not correct, although the reason about exchange of velocities is correct.

Therefore, the correct option is D.