Particles $P$ and $Q$, with masses $0.8\,\text{kg}$ and $0.5\,\text{kg}$ respectively, are fastened to the two ends of a light inextensible string that passes through a small hole in a smooth horizontal table of negligible thickness. $P$ travels on the upper surface of the table in a circular path with constant angular speed $6.25\,\text{rad s}^{-1}$.
(i)[4]
You are told that $Q$ is stationary and that the part of string attached to $Q$ is vertical. Calculate the radius of the path of $P$, and find the speed of $P$.
(ii)[6]
Instead, the section of string attached to $Q$ is inclined at $60^{\circ}$ to the vertical, and $Q$ moves below the table in a horizontal circular path, again with constant angular speed $6.25\,\text{rad s}^{-1}$. Calculate the total length of the string.
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