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(C) The angular frequency $\omega$ of a mass $m$ suspended from a wire of length $L$, area $A$, and Young's modulus $Y$ is given by $\omega = \sqrt{\f

Vedclass · Accepted Answer

$4$

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(C) The angular frequency $\omega$ of a mass $m$ suspended from a wire of length $L$, area $A$, and Young's modulus $Y$ is given by $\omega = \sqrt{\frac{YA}{mL}}$.Given: $m = 0.1 \,kg$, $L = 1 \,m$, $A = 4.9 	imes 10^{-7} \,m^2$, $\omega = 140 \,rad \,s^{-1}$.Squaring both sides: $\omega^2 = \frac{YA}{mL}$.Rearranging for $Y$: $Y = \frac{\omega^2 mL}{A}$.Substituting the values: $Y = \frac{(140)^2 	imes 0.1 	imes 1}{4.9 	imes 10^{-7}} = \frac{19600 	imes 0.1}{4.9 	imes 10^{-7}} = \frac{1960}{4.9 	imes 10^{-7}} = 400 	imes 10^7 = 4 	imes 10^9 \,N \,m^{-2}$.Comparing this with $n 	imes 10^9 \,N \,m^{-2}$, we get $n = 4$.

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