In an experiment,brass and steel wires of len | vedclass

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(D) Given: Length of each wire $\ell = 1\,m$,Area $A = 1\,mm^2 = 10^{-6}\,m^2$,Total elongation $\Delta \ell = 0.2\,mm = 0.2 	imes 10^{-3}\,m$. Young

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None of these

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(D) Given: Length of each wire $\ell = 1\,m$,Area $A = 1\,mm^2 = 10^{-6}\,m^2$,Total elongation $\Delta \ell = 0.2\,mm = 0.2 	imes 10^{-3}\,m$. Young's Modulus for steel $Y_s = 120 	imes 10^9\,N/m^2$ and for brass $Y_b = 60 	imes 10^9\,N/m^2$. Since the wires are in series,the force $F$ applied is the same for both. The total elongation is $\Delta \ell = \Delta \ell_s + \Delta \ell_b = \frac{F \ell}{A Y_s} + \frac{F \ell}{A Y_b} = \frac{F \ell}{A} \left( \frac{1}{Y_s} + \frac{1}{Y_b} ight)$. Stress $\sigma = \frac{F}{A} = \frac{\Delta \ell}{\ell \left( \frac{1}{Y_s} + \frac{1}{Y_b} ight)}$. Substituting the values: $\sigma = \frac{0.2 	imes 10^{-3}}{1 \left( \frac{1}{120 	imes 10^9} + \frac{1}{60 	imes 10^9} ight)} = \frac{0.2 	imes 10^{-3} 	imes 120 	imes 10^9}{1 + 2} = \frac{0.2 	imes 120 	imes 10^6}{3} = 8 	imes 10^6\,N/m^2$. Since $8 	imes 10^6\,N/m^2$ is not among the given options,the correct choice is $D$.

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