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) Numerical answer type. Work it out, then open the answer.

Answer: 05. Thermal stress σ = YαΔ T = 10¹¹ × 10⁻⁵ × 10 = 10⁷ Pa. Energy per unit length = 1/2(σ²)/(Y)A = 1/2 × 10¹⁴10¹¹ × 0.01 = 5 J/m

The area of cross-section of a railway track is 0.01 m2. The… | JEE Main 2021 (22 Jul, Shift 2)

Q53JEE Main 2021 · 22 JUL · SHIFT 2Difficult

Thermometry & Thermal Expansion

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 1011 Nm $^{-}$ 2)

Numerical answer type. Work it out, then open the answer.

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Answer: 05

Thermal stress $\sigma = Y\alpha\Delta T = 10^{11} \times 10^{-5} \times 10 = 10^7$ Pa.
Energy per unit length $= \dfrac{1}{2}\dfrac{\sigma^2}{Y}A = \dfrac{1}{2} \times \dfrac{10^{14}}{10^{11}} \times 0.01$
$= 5$ J/m

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Thermometry & Thermal Expansion question from JEE Main 2021 (22 Jul, Shift 2)

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