The area of cross-section of a railway track is $0.01\, {m}^{2}$. The temperature variation is $10^{\circ} {C}$. Coefficient of linear expansion of material of track is $10^{-5} /{ }^{\circ} {C}$. The energy stored per meter in the track is ...... ${J} / {m} .$
(Young's modulus of material of track is $10^{11} \,{Nm}^{-2}$ ))
JEE MAIN 2021, Medium
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Elastic energy $=\frac{Y}{2}(\text { strain })^{2} \times$ Area $\times$ length
Elastic energy per unit length $=\frac{Y}{2}(\text { strain })^{2} \times$ Area
$\left(\text { strain }=\frac{\Delta \ell}{\ell}=\alpha \Delta T=10^{-5} \times 10=10^{-4}\right)$
$=\frac{10^{11}}{2} \times\left(10^{-4}\right)^{2} \times 10^{-2}=5\, {J} / {m}$
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