A uniform metal rod of 2, mm^2 cross-section | vedclass

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Question

(A) The energy stored per unit volume $(u)$ in a stretched or compressed rod is given by the formula:$u = \frac{1}{2} 	imes Y 	imes (	ext{strain})^

Vedclass · Accepted Answer

$2880$

Vedclass · Answer

(A) The energy stored per unit volume $(u)$ in a stretched or compressed rod is given by the formula:$u = \frac{1}{2} 	imes Y 	imes (	ext{strain})^2$Since the rod is fixed between two walls,the thermal strain produced due to heating is given by:$	ext{strain} = \frac{\Delta L}{L} = \alpha \Delta 	heta$Given:$Y = 10^{11} \, N/m^2$$\alpha = 12 	imes 10^{-6} / ^oC$$\Delta 	heta = 20 - 0 = 20 \, ^oC$Substituting the values:$u = \frac{1}{2} 	imes 10^{11} 	imes (12 	imes 10^{-6} 	imes 20)^2$$u = \frac{1}{2} 	imes 10^{11} 	imes (240 	imes 10^{-6})^2$$u = \frac{1}{2} 	imes 10^{11} 	imes (2.4 	imes 10^{-4})^2$$u = \frac{1}{2} 	imes 10^{11} 	imes 5.76 	imes 10^{-8}$$u = 0.5 	imes 5760 = 2880 \, J/m^3$

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