Question

A uniform string of length $20 \,m$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is : (take $g\, = \,10\,ms^{-2}$)

• A. $2 \pi \sqrt{2} s$
• B. $2s$
• C. $2 \sqrt{2} s$
• D. $\sqrt{2} s$

Answer 1

Answer: (C)

$2 \sqrt{2} s$

Answer 2

$\frac{dy}{dt} = \sqrt{\frac{gy \rho A}{\mu}}$
$\frac{dy}{dt} = \int \sqrt{gy}$
$\int \frac{dy}{\sqrt{y}} = \sqrt{g} dt$
$\frac{y^{- \frac{1}{2}+1}}{-\frac{1}{2}+1}|^{l}_{0} = \sqrt{g } t |^{t}_{0}$
$t = 2 \sqrt{\frac{20}{10}} = 2 \sqrt{2} \sec$