The speed of a transverse wave passing through a string of length $50 \mathrm{~cm}$ and mass $10 \mathrm{~g}$ is $60 \mathrm{~ms}^{-1}$. The area of cross-section of the wire is $2.0 \mathrm{~mm}^{2}$ and its Young's modulus is $1.2 \times 10^{11} \mathrm{Nm}^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5} \mathrm{~m}$. The value of $x$ is __________.
Answer (integer)
15
Solution
$\mathrm{V}_{\mathrm{w}}=\sqrt{\frac{\mathrm{T}}{\mu}}$
<br/><br/>$60=\sqrt{\frac{\mathrm{T}}{10 \times 10^{-3}} \times 0.5}$
<br/><br/>$\mathrm{~T}=\frac{(60)^2 \times 10^{-2}}{0.5}=72 \mathrm{~N}$
<br/><br/>$\Delta \ell=\frac{\mathrm{F} \ell}{\mathrm{AY}}=\frac{72 \times 0.5}{2 \times 10^{-6} \times 1.2 \times 10^{11}}$
<br/><br/>$=\frac{72 \times 5}{24} \times 10^{-5}=15 \times 10^{-5}$
About this question
Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity
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