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Q.

The area of cross-section of a railway track is $0.01 m^{2}$ . The temperature variation is $10^{0} C$ Coefficient of linear expansion of material of track is $10^{- 5} /^{o} C$ . The energy stored per meter in the track is _______ J/m.
(Young's modulus of material of track is $10^{11} N m^{- 2}$ )

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answer is 5.

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Detailed Solution

Elastic energy $= \frac{Y}{2} {(s t r a i n)}^{2} \times A r e a \times l e n g t h$
$\Rightarrow$ Elastic energy per unit length $= \frac{Y}{2} {(s t r a i n)}^{2} \times A r e a$
$(s t r a i n = \frac{Δ l}{l} = α Δ T = 10^{- 5} \times 10 = 10^{- 4}) = \frac{10^{11}}{2} \times {(10^{- 4})}^{2} \times 10^{- 2} = 5 J / m$

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The area of cross-section of a railway track is 0.01m2. The temperature variation is 100C Coefficient of linear expansion of material of track is 10−5/oC. The energy stored per meter in the track is _______ J/m.(Young's modulus of material of track is 1011Nm−2)