4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d19c7390-0332-4cab-82e5-72976bd499a2-07_503_618_242_646}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A particle \(P\) of mass \(m\) is attached to one end of a light elastic string, of natural length \(2 a\) and modulus of elasticity \(6 m g\). The other end of the string is attached to a fixed point \(A\). The particle moves with constant speed \(v\) in a horizontal circle with centre \(O\), where \(O\) is vertically below \(A\) and \(O A = 2 a\), as shown in Figure 2 .
- Show that the extension in the string is \(\frac { 2 } { 5 } a\).
- Find \(v ^ { 2 }\) in terms of \(a\) and \(g\).