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Q.

The area of cross-section of a railway track is 0.01 m². 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 $10^{11} {Nm}^{- 2}$ )

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Detailed Solution

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

$\Rightarrow$ Elastic enrgy per unit length $= \frac{Y}{2}$ (strain)² $\times$ Area

$(strain = \frac{∆ l}{l} = α ∆ T = 10^{- 5} \times 10 = 10^{- 4})$

Elastic enrgy per unit length $= \frac{10^{11}}{2} \times {(10^{- 4})}^{2} \times 10^{- 2} = 5 J / m$

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The area of cross-section of a railway track is 0.01 m2. The temperature variation is 10∘C. Coefficient of linear expansion of material of track is 10-5 /∘C . The energy stored per meter in the track is _______J/m. (Young's modulus of material of track is 1011 Nm-2 )