when the apple moves in a horizontal circle, the tension force in the string provides the necessary centripetal force to move in circle. the tension in the string is given as
T=mv²/r
where T = tension force in the string , m = mass of the apple
v = speed of apple , r = radius of circle.
clearly , tension force depends on the square of the speed. hence greater the speed, greater will be the tension force.
at some point , the speed becomes large enough that it makes the tension force in the string becomes greater than the tensile strength of the string. at that point , the string breaks
