A massless rope of length $L$ has a small ball of mass $m$ attached to its midpoint and an identical ball of mass $m$ attached to its end. The rope is swung in a horizontal circle about its fixed other end with a constant angular velocity $\omega$. When $\omega$ is very large (so that the rope is nearly horizontal), let $h_1$ be the vertical depth of the middle mass below the pivot, and $h_2$ be the vertical depth of the end mass below the pivot. What is the ratio $h_1 / h_2$?