At the bottom of the circle, the ball is being pulled upward by tension in the rope and downward by its own weight, so that the net force on it is
∑ F = 450 N - (0.75 kg) g = (0.75 kg) a
where a is centripetal acceleration. At this maximum tension, the ball has a maximum centripetal acceleration of
a = (450 N - (0.75 kg) g) / (0.75 kg) = 590.2 m/s²
Then its maximum tangential speed v is such that
a = v² / (1.0 m)
⇒ v = √((1.0 m) a) ≈ 25 m/s
