It is my understanding (and ive just started studying this stuff so its very probable I've got the wrong end of the stick) that if you whirl a heavy object in a consistant orbit that the velocity and its mass (force) of the object being whirled around is always tangential to the point that the object is on the circle. Like if the string was cut - the ball would fly off at 90 degrees to the line of the centrifugal pull out.....
If the string gets cut the ball flies out in a straight line directly away from the source of the centripetal force that is trying to pull it inwards.