Question

The area of cross-section of a railway track is $0.01{\text{m}}^2$ . The temperature variation is $10{}^{\circ }\text{C}$. Coefficient of linear expansion of material of track is ${10}^{-5}{/}^{\circ }\text{C}$. The energy stored per meter in the track is ${\text{Jm}}^{-1}$. (Young's modulus of material of track is ${10}^{11}{\text{Nm}}^{-2})$

Answer 1

Elastic energy stored in the track$=\frac{Y}{2}(\text{strain}{)}^2\times$ Area $\times$ length

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

Here, $(\text{strain}=\frac{\Delta l}{l}=\alpha \Delta T={10}^{-5}\times 10={10}^{-4})$

$\Rightarrow E=\frac{{10}^{11}}{2}\times ({10}^{-4}{)}^2\times {10}^{-2}=5{\text{Jm}}^{-1}$

Correct answer: $5$