Q 11-05-157JEE MainJEE Main 2020 (9 Jan, Shift 1)Medium
Two particles of equal mass $m$ have respective initial velocities $u\hat{i}$ and $u\left(\dfrac{\hat{i} + \hat{j}}{2}\right)$. They collide completely inelastically. The energy lost in the process is:
Answer: (B) $\dfrac{1}{8}mu^2$
Initial kinetic energy: $\dfrac{1}{2}mu^2 + \dfrac{1}{2}m\cdot\dfrac{u^2}{2} = \dfrac{3}{4}mu^2$.
Momentum conservation for the combined mass $2m$:
$$\vec{V} = \frac{u\hat{i} + \frac{u}{2}(\hat{i} + \hat{j})}{2} = \frac{3u}{4}\hat{i} + \frac{u}{4}\hat{j}$$
Final kinetic energy: $\dfrac{1}{2}(2m)\left(\dfrac{9u^2}{16} + \dfrac{u^2}{16}\right) = \dfrac{5}{8}mu^2$.
Loss $= \dfrac{3}{4}mu^2 - \dfrac{5}{8}mu^2 = \dfrac{1}{8}mu^2$.
Solution by Sreeraj P, M.Sc Physics