Nuclear Fission & Fusion question from JEE Main 2024 (30 Jan, Shift 2)

Answer: (c)

1. Each daughter has mass $\tfrac{M}{3}$; by symmetry all three move with the same speed $v$ (total momentum stays zero).
2. Total kinetic energy $= \Delta M c^2$: $3\times\tfrac{1}{2}\cdot\tfrac{M}{3}v^2 = \tfrac{1}{2}Mv^2 = \Delta M c^2$.
3. $v = c\sqrt{\dfrac{2\Delta M}{M}}$.
4. So the answer is (c).