A ball of mass 0.2 kg attached to the end of a string of length 2.0 m is moving in a horizontal circ

Question

A ball of mass 0.2 kg attached to the end of a string of length 2.0 m is moving in a horizontal circle. The string will break if the tension is more than 40 N. What is the maximum speed with which the ball can be moved?

Professor PC Thomas Classes · Answer

Maximum tension provides the maximum centripetal force: $T_{max} = \frac{mv_{max}^2}{r}$. Rearranging for maximum speed: $v_{max} = \sqrt{\frac{T_{max} r}{m}} = \sqrt{\frac{40 	imes 2}{0.2}} = \sqrt{400} = 20 \mathrm{~m/s}$.