A uniform string of length 20m is suspended from a rigid support. A...

Velocity in a string, at a distance $x$, is given by

$v = \sqrt{\dfrac{µ gx}{µ}} = \sqrt{gx}$

$⇒ \dfrac{dx}{dt} = \sqrt{gx}$

$⇒ {∫}_{0}^{20}\dfrac{dx}{\sqrt{x}} = \sqrt{g}{∫}_{0}^{t}dt$

On integrating, we get,

$t = 2\sqrt{2}s$