Question

Speed of a transverse wave on a straight wire $(\text{mass}6.0g$, length $60cm$ and area of cross-section $1.0m{m}^2)$ is $90m/s$. If the Young's modulus of wire is $16\times {10}^{11}N/m^2$, the extension of wire over its natural length is

• A. $0.04mm$
• B. $0.03mm$
• C. $0.01mm$
• D. $0.02mm$

Answer 1

The correct option is B $0.03mm$

Given, mass of the wire,

$m=6g=6\times {10}^{-3}kg$

Length of the wire, $l=60cm=0.6m$

Area of cross section,

$A=1m{m}^2={10}^{-6}{m}^2$

Speed of the transverse wave, $v=90m/s$

And Young's modulus of the wire,

$Y=16\times {10}^{11}N/m^2$,

As we know, speed of transverse wave in the wire, $v=\sqrt{\frac{T}{\mu }}$

$v=\sqrt{\frac{\frac{YA\Delta l}{l}}{\frac{m}{l}}}$

$90=\sqrt{\left(\frac{16\times {10}^{11}\times {10}^{-6}\times \Delta l}{6\times {10}^{-3}}\right)}$

$\Delta l=\frac{8100\times 3}{8}\times {10}^{-8}=0.03mm$

Final answer : (c)