The iron ball shown is being swung in a vertical circle at the end of a 0.7-m string. how slowly can the ball go through its top position without having the string go slack?

A centripetal force is a force which keeps an object moving in a circle. When the ball is at the top position, let's assume that the speed v is such that the gravitational force is precisely equal to the required centripetal force to keep the ball moving around in a circle. Then the string will not go slack. centripetal force = force of gravity on the ball m v^2 / r = m g v^2 / r = g v^2 = g r v = sqrt { g r } v = sqrt { (9.80~m/s^2) (0.7 m) } v = 2.62 m/s The minimum speed of the ball at the top position is 2.62 m/s