Tension in a Uniform Thread!

Classical Mechanics Level 4

A uniform flexible chain of mass \(m\) and length \(L (\leq \frac{\pi R}{2})\) rests on a fixed smooth cylindrical surface of radius \(R\) such that one end \(A\) of the chain is at the top of the cylinder while the other end \(B\) is free. The chain is held stationary by a horizontal thread \(PA\) as shown in the figure. Calculate the Tension \((T)\) in the thread.

Assume \(\alpha = \dfrac L R \).

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