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) $c\sqrt{\dfrac{2\Delta m}{M}}$
By momentum conservation the two equal daughters move with equal speeds $v$ in opposite directions. The released energy becomes their kinetic energy:
$$\Delta m\,c^2 = 2 \times \frac{1}{2}\cdot\frac{M}{2}v^2 \;\Rightarrow\; v = c\sqrt{\frac{2\Delta m}{M}}$$
Solution by Sreeraj P, M.Sc Physics