Q 11-04-019NEETJEE MainEAMCET 2009 (Engineering)Medium
A particle of mass $4m$ at rest explodes into three pieces of masses $m$, $m$ and $2m$. The equal masses move along the $X$-axis and $Y$-axis with velocities $4\ \text{m s}^{-1}$ and $6\ \text{m s}^{-1}$ respectively. The magnitude of the velocity of the heavier mass is
Answer: (B) $\sqrt{13}\ \text{m s}^{-1}$
Concept. Initial momentum is zero, so the heavy piece balances the other two.
Step 1. Momentum. $2mv_3 = \sqrt{(4m)^2 + (6m)^2} = 2\sqrt{13}m$.
Step 2. Speed. $v_3 = \sqrt{13}$ m/s.
Answer. $\sqrt{13}\ \text{m s}^{-1}$ (Option B).
Solution by Sreeraj P, M.Sc Physics