The speed of a transverse wave passing through a string of length $50 \;cm$ and mass $10\,g$ is $60\,ms ^{-1}$. The area of cross-section of the wire is $2.0\,mm ^{2}$ and its Young's modulus is $1.2 \times 10^{11}\,Nm ^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5}\; m$. The value of $x$ is $...$
JEE MAIN 2022, Medium
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$V _{ T }=\sqrt{\frac{ T }{\mu}}$
$60=\sqrt{\frac{ T }{10 \times 10^{-3}} \times 0.5}$
$T =\frac{(60)^{2} \times 10^{-2}}{0.5}=72\,N$
$\Delta \ell=\frac{ F \ell}{ AY }=\frac{72 \times 0.5}{2 \times 10^{-6} \times 1.2 \times 10^{11}}$
$=\frac{72 \times 5}{24} \times 10^{-5}=15 \times 10^{-5}$
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