3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f6ab162c-8473-4464-ad62-87a359d85ab3-04_707_1006_258_427}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Two particles \(P\) and \(Q\), of mass \(m\) and \(2 m\) respectively, are attached to the ends of a light inextensible string of length 6l. The string passes through a small smooth fixed ring at the point \(A\). The particle \(Q\) is hanging freely at a distance \(l\) vertically below \(A\). The particle \(P\) is moving in a horizontal circle with constant angular speed \(\omega\). The centre \(O\) of the circle is vertically below \(A\). The particle \(Q\) does not move and \(A P\) makes a constant angle \(\theta\) with the downward vertical, as shown in Figure 2.
Show that
- \(\theta = 60 ^ { \circ }\)
- \(\omega = \sqrt { } \left( \frac { 2 g } { 5 l } \right)\)