Question

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

• A. $6.6\times 10^7$ Pa
• B. $8.8\times 10^7$ Pa
• C. $3.3\times 10^7$ Pa
• D. $5.5\times 10^7$ Pa

Answer 1

Answer: (C)

As the steel rail is contrained from expansion, the expansion pressure causes stress in the steel rail.
Thermal stress depends upon coefficient of expansion a and rise of temperature $\Delta T$
$\therefore$ Thermal stress $\sigma \propto \alpha \Delta T$
$\Rightarrow \sigma =Y\cdot \alpha \cdot \Delta T$ (where, $Y=$ Young's modulus)
$\therefore \sigma =2\times 10^{11}\times 11\times 10^{-5}\times (40-25)$
$=3.3\times 10^{7}Pa$