Question

The area of cross-section of a railway track is $0.01m^2$. 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 $10^{11}N{m}^{-2}$ )

Answer 1

Answer: 5

Elastic energy $=\frac{Y}{2}(\text{ strain }{)}^2\times$ Area $\times$ length
$\Rightarrow$ Elastic energy per unit length $=\frac{Y}{2}(\text{ strain }{)}^2\times$ Area
$($ strain $=\frac{\Delta l}{l}=\alpha \Delta T=10^{-5}\times 10=10^{-4})$
$=\frac{10^{11}}{2}\times {\left(10^{-4}\right)}^2\times 10^{-2}=5J/m$