Question #42352

A heavy parent nucleus is modeled as a rigid thin rod of length $L$ with a non-uniform linear mass density $\lambda(x) = \lambda_0\left(1 + \frac{2x}{L}\right)$ for $0 \le x \le L$. It is initially rotating with a constant angular velocity $\omega$ about an axis perpendicular to the rod passing through its geometric center, which is at rest in the laboratory frame. The nucleus undergoes fission by splitting exactly at its geometric center into two fragments. The binding energy per unit mass of the parent nucleus is $B_1$ and that of both fragments is $B_2$ ($B_2 > B_1$). Assume all available energy in the center-of-mass (COM) frame is converted entirely into the relative translational kinetic energy of the fragments. What is the relative speed $v_{rel}$ of the two fragments immediately after fission?