3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{00388805-5d60-4327-a10e-c0df74a0cb75-05_776_791_223_573}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
A small ball \(P\) of mass \(m\) is attached to the midpoint of a light inextensible string of length \(4 l\). The ends of the string are attached to fixed points \(A\) and \(B\), where \(A\) is vertically above \(B\). Both strings are taut and \(A P\) makes an angle of \(30 ^ { \circ }\) with \(A B\), as shown in Figure 1. The ball is moving in a horizontal circle with constant angular speed \(\omega\).
- Find, in terms of \(m , g , l\) and \(\omega\),
- the tension in \(A P\),
- the tension in \(B P\).
- Show that \(\omega ^ { 2 } \geqslant \frac { g \sqrt { 3 } } { 3 l }\).