You attach one end of a string of length (ell) to a small ball of inertia (m).

Question:

You attach one end of a string of length $\ell$ to a small ball of inertia $m$. You attach the string's other end to a pivot that allows free revolution. You hold the ball out to the side with the string taut along a horizontal line, as in Figure P11.29.

(a) If you release the ball from rest, what is the tension $\mathcal{T}$ in the string as a function of the angle $\theta$ swept through? $(b)$ What maximum tension should the string be able to sustain if you want it not to break through the ball's entire motion?

Data from Figure P11.29

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