3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{45c51316-7d58-4c16-9b5f-1d7421060a88-3_485_855_1073_584}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{figure}
A particle \(P\) of mass \(m\) is attached to one end of a light inextensible string of length \(3 a\). The other end of the string is attached to a fixed point \(A\) which is a vertical distance \(a\) above a smooth horizontal table. The particle moves on the table in a circle whose centre \(O\) is vertically below \(A\), as shown in Fig. 1. The string is taut and the speed of \(P\) is \(2 \sqrt { } ( a g )\).
Find
- the tension in the string,
- the normal reaction of the table on \(P\).