$\mathrm{v}=\sqrt{\frac{\mathrm{T}}{\mu}}$ $...(I)$
where $\mu=\frac{\mathrm{m}}{1}=\frac{\text { mass of string }}{\text { length of string }}$
The tension $\mathrm{T}=\frac{\mathrm{m}}{\ell} \times \mathrm{x} \times \mathrm{g}$ $...(II)$
From $(a)$ and $(b)$
$\frac{d x}{d t}=\sqrt{g x}$
$\mathrm{x}^{-1 / 2} \mathrm{dx}=\sqrt{\mathrm{g}} \mathrm{dt} \quad \therefore \int_{0}^{\ell} \mathrm{x}^{-1 / 2} \mathrm{dx}-\sqrt{\mathrm{g}} \int_{0}^{\ell} \mathrm{dt}$
$2 \sqrt{l}=\sqrt{g} \times t \quad \therefore t=2 \sqrt{\frac{\ell}{g}}=2 \sqrt{\frac{20}{10}}=2 \sqrt{2}$
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