A steel rod of length $1\,m$ and cross sectional area $10^{-4}\,m ^2$ is heated from $0^{\circ}\,C$ to $200^{\circ}\,C$ without being allowed to extend or bend. The compressive tension produced in the rod is $........\times 10^4\,N$ (Given Young's modulus of steel $=2 \times 10^{11}\,Nm ^{-2}$, coefficient of linear expansion $=10^{-5}\, K ^{-1}$.
JEE MAIN 2023, Easy
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$\text { Stress }=Y \times \text { strain }$
$\text { Stress }=Y \times \frac{\Delta \ell}{\ell}$
$= Y \times \frac{\ell \alpha \Delta T }{\ell}= Y \alpha \Delta T$
$\text { Compressive Tension }=\text { Stress } \times \text { Area of cross section }$
$= YA \alpha \Delta T =4 \times 10^4\,N$
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