Solve this following


The area of cross-section of a railway track is $0.01 \mathrm{~m}^{2}$. The temperature variation is $10^{\circ} \mathrm{C}$. Coefficient of linear expansion of material of track is $10^{-5} /{ }^{\circ} \mathrm{C}$. The energy stored per meter in the track is $\mathrm{J} / \mathrm{m}$.

(Young's modulus of material of track is $10^{11} \mathrm{Nm}^{-2}$ )


Elastic energy $=\frac{\mathrm{Y}}{2}(\text { strain })^{2} \times$ Area $\times$ length

$\Rightarrow \quad$ Elastic energy per unit length $=\frac{\mathrm{Y}}{2}(\text { strain })^{2} \times$ Area

$\left(\operatorname{strain}=\frac{\Delta \ell}{\ell}=\alpha \Delta \mathrm{T}=10^{-5} \times 10=10^{-4}\right)$

$=\frac{10^{11}}{2} \times\left(10^{-4}\right)^{2} \times 10^{-2}=5 \mathrm{~J} / \mathrm{m}$


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