Assuming the ball is swung around in a circle parallel to the ground, it has a centripetal acceleration a of
a = v ² / R
where v is the tangential speed of the ball and R is the length of the string.
The tension in the string is 0.5 N, so by Newton's second law, the ball has acceleration
F = m a → a = F / m = (0.5 N) / (0.1 kg) = 5 m/s²
where m is the ball's mass.
Solve for R :
a = v ² / R → R = v ² / a = (2 m/s)² / (5 m/s²) = 0.8 m = 80 cm
