6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8b85b908-bb74-4532-a1b4-3826946bd43b-4_437_364_196_717}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{figure}
The two ends of a light inextensible string of length \(3 a\) are attached to fixed points \(Q\) and \(R\) which are a distance of \(a \sqrt { } 3\) apart with \(R\) vertically below \(Q\). A particle \(P\) of mass \(m\) is attached to the string at a distance of \(2 a\) from \(Q\).
\(P\) is given a horizontal speed, \(u\), such that it moves in a horizontal circle with both sections of the string taut as shown in Figure 3.
- Show that \(\angle P R Q\) is a right angle.
- Find \(\angle P Q R\) in degrees.
- Find, in terms of \(a , g , m\) and \(u\), the tension in the section of string
- \(P Q\),
- \(P R\).
- Show that \(u ^ { 2 } \geq \frac { g a } { \sqrt { 3 } }\).