A ring of mass M is suspended by a thread and two balls of mass m are free to slide without friction along this ring. The two balls are released simultaneously from the top of the ring and slide along it in opposite directions (see the figure below). Show that the ring will rise at some point ifm>23M? and that the angle ? at which this occurs is given by:cos(?)?3(1?1+2m3M??)? Hint: the ring rises when the force exerted by the two balls on the ring compensates exactly gravity. The normalN that the ring exerts on each ball is equal and opposite to the force that each ball exerts on the ring. T

his forceN contributes, with gravity, to the force centripetal that each ball feels.

m m M FIGURE 1