5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{9777abb8-a564-40d5-8d96-d5649913737b-16_730_634_246_657}
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\caption{Figure 2}
\end{figure}
A small smooth ring \(R\) of mass \(m\) is threaded on to a thin smooth fixed vertical pole. One end of a light inextensible string of length \(2 l\) is attached to a point \(A\) on the pole. The other end of the string is attached to \(R\). A particle \(P\) of mass \(m\) is attached to the midpoint of the string. The particle \(P\) moves with constant angular speed in a horizontal circle, with both halves of the string taut, and \(A R = \frac { 6 l } { 5 }\), as shown in Figure 2.
It may be assumed that in this motion the string does not wrap itself around the pole and that at any instant, the triangle \(A P R\) lies in a vertical plane.
- Show that the tension in the lower half of the string is \(\frac { 5 m g } { 3 }\)
- Find, in terms of \(l\) and \(g\), the time for \(P\) to complete one revolution.