Q 11-05-200JEE MainJEE Main 2018 (8 Apr)Medium
In a collinear collision, a particle with an initial speed $v_0$ strikes a stationary particle of the same mass. If the final total kinetic energy is $50\%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after the collision, is:
Answer: (C) $\sqrt2\,v_0$
Momentum: $v_1 + v_2 = v_0$. Energy: $v_1^2 + v_2^2 = 1.5v_0^2$.
$$(v_1 - v_2)^2 = 2(v_1^2 + v_2^2) - (v_1 + v_2)^2 = 3v_0^2 - v_0^2 = 2v_0^2$$
$$|v_1 - v_2| = \sqrt2\,v_0$$
Solution by Sreeraj P, M.Sc Physics