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
