A particle of mass m is attached to the highest point of a smooth rigid sphere of radius a by a light inextensible string of length πa/4. The particle moves in contact with the outer surface of the sphere, with the string taut, and describes a horizontal circle with constant speed u. Find the reaction of the sphere on the particle and the tension in the string. Deduce the maximum value of u for which such a motion could take place. What will happen if u exceeds this value?