Speed of a transverse wave on a straight wire (mass $6.0$
$\mathrm{g}$, length $60 \mathrm{~cm}$ and area of cross-section $1.0 \mathrm{~mm}^{2}$ ) is
$90 \mathrm{~ms}^{-1}$. If the Young's modulus of wire is $16 \times 10^{11} \mathrm{Nm}^{-2}$
the extension of wire over its natural length is:
Correct Option: 1
(1) Given, $l=60 \mathrm{~cm}, m=6 \mathrm{~g}, A=1 \mathrm{~mm}^{2}, v=90 \mathrm{~m} / \mathrm{s}$ and $Y=16 \times 10^{11} \mathrm{Nm}^{-2}$Again from, $Y=\frac{T}{A} \Delta L / L_{0}$
Again from, $Y=\frac{T}{A} \Delta L / L_{0}$
$\Delta L=\frac{T l}{Y A}=\frac{m v^{2} \times l}{l(\mathrm{YA})}$
$=\frac{6 \times 10^{-3} \times 90^{2}}{16 \times 10^{11} \times 10^{-6}}=3 \times 10^{-4} \mathrm{~m}$
$=0.03 \mathrm{~mm}$
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