2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7ecb33af-c165-4b72-98f2-7574fad3fdd5-04_506_613_246_671}
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\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 mg . 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 \(g\).
[0pt]
[Question 2 Continued]