JEE Main · 2010 · 11 Apr 2010 · Offline · Modern Physics

The parent is at rest, so by conservation of momentum the two equal fragments fly apart with equal and opposite velocities of the same speed $V$. The mass lost in the decay, $\Delta m$, reappears as the kinetic energy of the two fragments: $\Delta m{c}^2=2\times \frac{1}{2}\frac{M}{2}{V}^2=\frac{M}{2}{V}^2$. Solving, $V^2=\frac{2\Delta m{c}^2}{M}$, so $V=c\sqrt{\frac{2\Delta m}{M}}$.