A particle P of mass m slides on a smooth horizontal table. P is connected to a second particle Q of mass M by a light inextensible string which passes through a small smooth hole O in the table, so that Q hangs below the table while P moves on top. Investigate motions of this system in which Q remains at rest vertically below O, while P describes a circle with centre O and radius b. Show that this is possible provided that P moves with constant speed u, where u2=Mgb/m.