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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 $\mathrm{x \times 10^{-5} \mathrm{~m}}$ . The value of $\mathrm{x }$ is___________.
Option: 1
15

Option: 2
-

Option: 3
-

Option: 4
-

Answers (1)

best_answer

$\mathrm{\ell=0.5 \mathrm{~m} }$

$\mathrm{m=10 g=10^{-2} \mathrm{~kg} }$

$\mathrm{V=60 \frac{\mathrm{m}}{\mathrm{s}}=\sqrt{\frac{\mathrm{T}}{\mathrm{\mu }}} }$

$\mathrm{A=2 \times 10^{-6} \mathrm{~m}^2 }$

$\mathrm{Y=1.2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2 }$

$\mathrm{\Delta \ell=x \times 10^{-5} \mathrm{~m} }$

$\mathrm{\mu V^2=T }$

$\mathrm{\left(\frac{10^{-2}}{0.5}\right)(60)^2 =T }$

$\mathrm{\frac{36}{0.5} =T }$

$\mathrm{T=72 \mathrm{H} }$

$\mathrm{Y=\frac{F}{A} \times \frac{\ell}{\Delta \ell} }$

$\mathrm{1.2 \times 10^{11} =\frac{72}{2 \times 10^{-6}} \times \frac{0.5}{x \times 10^{-5}} }$

$\mathrm{x =\frac{18}{1.2} }$

$\mathrm{x =15}$

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