2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{dceb2432-117c-40fe-bf3d-782beeb42e41-04_424_510_246_767}
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\caption{Figure 2}
\end{figure}
A light elastic string \(A B\) has modulus of elasticity \(2 m g\) and natural length \(k a\), where \(k\) is a constant.
The end \(A\) of the elastic string is attached to a fixed point. The other end \(B\) is attached to a particle of mass \(m\). The particle is held in equilibrium, with the elastic string taut, by a force that acts in a direction that is perpendicular to the string. The line of action of the force and the elastic string lie in the same vertical plane. The string makes an angle \(\theta\) with the downward vertical at \(A\), as shown in Figure 2.
Given that the length \(A B = \frac { 21 } { 10 } a\) and \(\tan \theta = \frac { 3 } { 4 }\), find the value of \(k\).