Question

A uniform rope of mass $0.1kg$ and length $2.45m$ hangs from a ceiling. The time taken by the transverse wave to travel through the full length of the rope is

• A. $2.0s$
• B. $1.2s$
• C. $1.0s$
• D. $2.2s$

Answer 1

Answer: (C)

$1.0s$

$T=\left(\frac{M}{L}x\right)gandv=\sqrt{\frac{\frac{Mx}{L}g}{\mu /L}}=\sqrt{gx}$
$v=\frac{dx}{dt}=\sqrt{gx}ordt=\frac{dx}{\sqrt{gx}}$
$ort=\frac{1}{\sqrt{g}}{\int }_0^L{x}^{-1/2}dx$
$ort=2\sqrt{\frac{L}{g}}=2\sqrt{\frac{2.45}{9.8}}=1s$