6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2e837bb9-4ada-4f0f-8b21-2730611335f2-20_499_748_244_653}
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\caption{Figure 4}
\end{figure}
A particle \(P\) of mass \(m\) is attached to one end of a light inextensible string of length \(a\). The other end of the string is attached to a fixed point \(O\). The particle is held at the point \(A\), where \(O A = a\) and \(O A\) is horizontal, as shown in Figure 4.
The particle is projected vertically downwards with speed \(\sqrt { \frac { 9 a g } { 5 } }\)
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 \(S\).
- Show that \(S = \frac { 3 } { 5 } m g ( 5 \cos \theta + 3 )\)
At the instant when the string becomes slack, the speed of \(P\) is \(v\)
- Show that \(v = \sqrt { \frac { 3 a g } { 5 } }\)
- Find the maximum height of \(P\) above the horizontal level of \(O\)