Two beads, each of mass m, are free to slide on a rigid, vertical hoop of mass m_{h}. The beads are threaded on the hoop so that they cannot fall off of the hoop. They are released with negligible velocity at the top of the hoop and slide down to the bottom in opposite directions. The hoop remains vertical at all times. What is the maximum value of the ratio \mathrm{m} / \mathrm{m}_{h} such that the hoop always remains in contact with the ground? Neglect friction.
