Mechanical Properties of Solids

JEE Main level, numerical answer, medium

113 of 118

Question 113 of 118

The area of cross-section of a railway track is 0.01m2.0.01{m}^{2}. The temperature variation is 10∘C.10^{\circ}C. Coefficient of linear expansion of material of track is 10−5C−1∘.{10}^{-5}C-1^{\circ}. The energy stored per meter in the track is Jm−1.J{m}^{-1}. (Young's modulus of material of track is 1011Nm−2{10}^{11}N{m}^{-2})

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Answer: 5

Elastic energy =Y2(strain)2×=\dfrac{Y}{2}(strain{)}^{2}\times Area ×\times length
⇒\Rightarrow Elastic energy per unit length =Y2(strain)2×=\dfrac{Y}{2}(strain{)}^{2}\times Area
((strain =Δℓℓ=αΔT=10−5×10=10−4)=\dfrac{\Delta \ell }{\ell }=\alpha \Delta T={10}^{-5}\times 10={10}^{-4})
=10112×(10−4)2×10−2=5Jm−1=\dfrac{{10}^{11}}{2}\times {\left({10}^{-4}\right)}^{2}\times {10}^{-2}=5J{m}^{-1}

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