2 A particle P of mass 0.3 kg is connected to a fixed point O by a light inextensible string of length 4.2 m . Firstly, P is moving in a horizontal circle as a conical pendulum, with the string making a constant angle with the vertical. The tension in the string is 3.92 N .

1. Find the angle which the string makes with the vertical.
2. Find the speed of P . P now moves in part of a vertical circle with centre O and radius 4.2 m . When the string makes an angle \(\theta\) with the downward vertical, the speed of P is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) (see Fig. 2). You are given that \(v = 8.4\) when \(\theta = 60 ^ { \circ }\). \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{2a4afead-e772-4d86-bc8d-86ffa5bca507-2_382_648_1985_751} \captionsetup{labelformat=empty} \caption{Fig. 2}
   \end{figure}
3. Find the tension in the string when \(\theta = 60 ^ { \circ }\).
4. Show that \(v ^ { 2 } = 29.4 + 82.32 \cos \theta\).
5. Find \(\theta\) at the instant when the string becomes slack.