Question

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 $10^{11} Nm ^{-2}$ )

Answer 1

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
$\left(\right.$ strain $\left.=\frac{\Delta l}{l}=\alpha \Delta T=10^{-5} \times 10=10^{-4}\right)$
$=\frac{10^{11}}{2} \times\left(10^{-4}\right)^{2} \times 10^{-2}=5 \,J / m$