5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4c1c51ff-6ae8-402d-b303-b656d26e4230-07_842_449_248_826}
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\caption{Figure 3}
\end{figure}
A particle \(P\) of mass \(m\) is attached to the ends of two light inextensible strings. The other ends of the strings are attached to fixed points \(A\) and \(B\), where \(B\) is vertically below \(A\) and \(A B = l\). The particle is moving with constant angular speed \(\omega\) in a horizontal circle. Both strings are taut and inclined at \(30 ^ { \circ }\) to \(A B\), as shown in Figure 3.
- Show that the tension in \(A P\) is \(\frac { m \sqrt { 3 } } { 6 } \left( 2 g + l \omega ^ { 2 } \right)\)
- Find the tension in \(B P\).
- Show that the time taken by \(P\) to complete one revolution is less than \(\pi \sqrt { \frac { 2 l } { g } }\)