In the picture L1 is shorter than L2. I set the change in kinetic energy equal to the negative change in gravitational potential energy, with the final height (of the center of mass of the rope) being L/2 and the initial height being L2/2 + L1:
(1/2)mv^2 = mg(L/2 – L2/2 – L1)
The masses cancel and I got that v = √(gL1)
I’m just asking about this because setting the heights right in terms of L, L1 and L2 is slightly confusing, and the question seems to ask for an actual speed but I think you can only find it in terms of the length.