6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d93ae982-9395-4311-9972-be727b3ce954-18_483_730_242_609}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
A particle \(P\) of mass \(m\) is attached to one end of a light inextensible string of length \(l\). The other end of the string is attached to a fixed point \(O\). The particle is held at the point \(A\), where \(O A = l\) and \(O A\) is horizontal. The particle is then projected vertically downwards from \(A\) with speed \(\sqrt { 2 g l }\), as shown in Figure 4 . When the string makes an angle \(\theta\) with the downward vertical through \(O\) and the string is still taut, the tension in the string is \(T\).
- Show that \(T = m g ( 3 \cos \theta + 2 )\)
At the instant when the particle reaches the point \(B\), the string becomes slack.
- Find the speed of \(P\) at \(B\).
- Find the greatest height above \(O\) reached by \(P\) in the subsequent motion.