Q 12-13-013JEE MainAIEEE 2010Medium
A nucleus of mass $M + \Delta m$ is at rest and decays into two daughter nuclei of equal mass $\dfrac{M}{2}$ each. The speed of light is $c$. The speed of each daughter nucleus is
Answer: (B) $c\sqrt{\dfrac{2\Delta m}{M}}$
Concept. The mass loss $\Delta m$ appears as kinetic energy; the two equal pieces move with equal speeds (momentum).
Step 1. Energy. $\Delta mc^2=2\times\tfrac12\cdot\dfrac M2v^2=\dfrac{Mv^2}{2}$.
Step 2. Speed. $v=c\sqrt{\dfrac{2\Delta m}{M}}$.
Answer. Option B.
Solution by Sreeraj P, M.Sc Physics
