The Young's modulus of a steel wire of length | vedclass

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(C) Given:Length $L = 6\,m$Area $A = 3\,mm^2 = 3 	imes 10^{-6}\,m^2$Young's modulus $Y = 2 	imes 10^{11}\,N/m^2$Mass $m = 4\,kg$Gravity on Earth $g_

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$0.1\,mm$

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(C) Given:Length $L = 6\,m$Area $A = 3\,mm^2 = 3 	imes 10^{-6}\,m^2$Young's modulus $Y = 2 	imes 10^{11}\,N/m^2$Mass $m = 4\,kg$Gravity on Earth $g_e = 10\,m/s^2$Gravity on planet $g_p = \frac{1}{4} g_e = \frac{10}{4} = 2.5\,m/s^2$The tension $F$ in the wire is equal to the weight of the block on the planet:$F = m 	imes g_p = 4 	imes 2.5 = 10\,N$The formula for elongation $\Delta L$ is:$\Delta L = \frac{FL}{AY}$Substituting the values:$\Delta L = \frac{10 	imes 6}{3 	imes 10^{-6} 	imes 2 	imes 10^{11}}$$\Delta L = \frac{60}{6 	imes 10^5} = 10 	imes 10^{-5} = 10^{-4}\,m$Converting to millimeters:$\Delta L = 10^{-4} 	imes 10^3\,mm = 0.1\,mm$

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