A horizontal steel railroad track has a length of $ 100 \mathrm{~m} $ when the temperature is $ 25^{\circ} \mathrm{C} $. The track is constrained from expanding or bending. The stress on the track on a hot summer day, when the temperature is $ 40^{\circ} \mathrm{C} $, is (Note: The linear coefficient of thermal expansion for steel is $ 1.1 \times 10^{-5} \mathrm{CC}^{-1} $ anc the Young's modulus of steel is $ 2 \times 10^{11} \mathrm{~Pa} $ )

Question

A horizontal steel railroad track has a length of $ 100 \mathrm{~m} $ when the temperature is $ 25^{\circ} \mathrm{C} $. The track is constrained from expanding or bending. The stress on the track on a hot summer day, when the temperature is $ 40^{\circ} \mathrm{C} $, is (Note: The linear coefficient of thermal expansion for steel is $ 1.1 \times 10^{-5} \mathrm{CC}^{-1} $ anc the Young's modulus of steel is $ 2 \times 10^{11} \mathrm{~Pa} $ ), $ 6.6 \times 10^{7} \mathrm{~Pa} $, $ 8.8 \times 10^{7} \mathrm{~Pa} $, $ 3.3 \times 10^{7} \mathrm{~Pa} $, $ 5.5 \times 10^{7} \mathrm{~Pa} $

MARKS App · Accepted Answer

The stress is, F A = Y × α × ∆ T . where, Y is Young's modulus, α is coefficient of thermal expansion & ∆ T is change in temperature. ∴ Stress = 2 × 10 11 × 1 . 1 × 10 - 5 × 40 - 25 ∴ Stress = 3 . 3 × 10 7 Pa

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