Question

The speed of a traverse wave travelling on a wire having a length $50cm$ and mass $50g$ is $80m{s}^{-1}$. The area of cross-section of the wire is $1m{m}^2$ and its Young's modulus is $16\times {10}^{11}N{m}^{-2}$. Find the extension of the wire over natural length.

• A. $2cm$
• B. $2mm$
• C. $0.2mm$
• D. $0.02mm$

Answer 1

The correct option is C $0.2mm$

$v=\sqrt{\frac{T}{\mu }}$
$orT=v^2\mu =(80{)}^2\left(\frac{50}{0.5}\times {10}^{-3}\right)=640N$
$andY=\frac{Fl}{A△l}$

$or△l=\frac{Fl}{AY}=\frac{640\times 0.5}{{10}^{-6}\times 16\times {10}^{11}}=20\times {10}^{-5}m$