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(B) The speed of a transverse wave in a string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.Li

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(B) The speed of a transverse wave in a string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.Linear mass density $\mu = \frac{m}{L} = \frac{10 	imes 10^{-3} \; kg}{0.5 \; m} = 0.02 \; kg/m$.Given $v = 60 \; ms^{-1}$,we have $60 = \sqrt{\frac{T}{0.02}}$,which implies $T = 3600 	imes 0.02 = 72 \; N$.The extension $\Delta L$ is given by Hooke's Law: $\Delta L = \frac{TL}{AY}$.Substituting the values: $A = 2.0 \; mm^2 = 2.0 	imes 10^{-6} \; m^2$,$L = 0.5 \; m$,$Y = 1.2 	imes 10^{11} \; Nm^{-2}$.$\Delta L = \frac{72 	imes 0.5}{2.0 	imes 10^{-6} 	imes 1.2 	imes 10^{11}} = \frac{36}{2.4 	imes 10^5} = 15 	imes 10^{-5} \; m$.Comparing this with $x 	imes 10^{-5} \; m$,we get $x = 15$.

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