At any instant

$T \cos \theta=m g………(i)$

$T \sin \theta=F_{e}………(ii)$

$\Rightarrow \quad \frac{\sin \theta}{\cos \theta}=\frac{F_{e}}{m g} \Rightarrow \mathrm{F}_{\mathrm{e}}=\mathrm{mg} \tan \theta$

$\Rightarrow \quad \frac{k q^{2}}{x^{2}}=m g \tan \theta \Rightarrow q^{2} \propto x^{2} \tan \theta$

$\sin \theta =\frac{x}{2 l} $

For small  $\theta$, $\sin \theta \approx \tan \theta  $

$\therefore q^{2} \propto x^{3}$

$\Rightarrow \quad q \frac{d q}{d t} \propto x^{2} \frac{d x}{d t}$

$\therefore \quad \frac{d q}{d t}=$ const.

$\therefore \quad q \propto x^{2}, v \Rightarrow x^{3 / 2} \alpha x^{2}, v\left[\because q^{2} \propto x^{3}\right]$

$\Rightarrow v \propto x^{-1 / 2}$