A uniform ideal spring with spring constant \(k\) and unstretched length \(L\) is suspended vertically from a fixed ceiling. A block of mass \(m\) is attached to the lower end of the spring and gently lowered until it hangs at rest in equilibrium, storing an elastic potential energy \(U_1\) in the spring. The block is then removed, and the spring is cut into two equal halves. One of these half-length springs is suspended from the ceiling, and the same block of mass \(m\) is attached and gently lowered to equilibrium, storing an elastic potential energy \(U_2\). What is the ratio \(\dfrac{U_2}{U_1}\)?