6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2c0bb9ea-31a6-42f1-9e2e-d792eee8fd10-09_1089_1072_278_466}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
A light inextensible string of length \(14 a\) has its ends attached to two fixed points \(A\) and \(B\), where \(A\) is vertically above \(B\) and \(A B = 10 a\). A particle of mass \(m\) is attached to the string at the point \(P\), where \(A P = 8 a\). The particle moves in a horizontal circle with constant angular speed \(\omega\) and with both parts of the string taut, as shown in Figure 3.
- Show that angle \(A P B = 90 ^ { \circ }\).
- Show that the time for the particle to make one complete revolution is less than
$$2 \pi \sqrt { \left( \frac { 32 a } { 5 g } \right) } .$$