A horizontal steel railroad track has a length of $100 \,m$, 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 ............. $\times 10^7\,Pa$ (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 $2 \times 10^{11} \,Pa$ )
KVPY 2015, Medium
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(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 $\alpha$ 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)
$\therefore \sigma =2 \times 10^{11} \times 11 \times 10^{-5} \times(40-25)$
$=3.3 \times 10^7 \,Pa$
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