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JEE MAIN 2021
01-09-21 S2
Question
A steel rod with $y=2.0 \times 10^{11} \mathrm{Nm}^{-2}$ and $\alpha=10^{-5} \mathrm{C}^{-1}$ of length 4 m and area of cross-section $10 \mathrm{~cm}_2$ is heated from $0^{\circ} \mathrm{C}$ to $400^{\circ} \mathrm{C}$ without being allowed to extend. The tension produced in the rod is $\mathrm{x} \times 10^5 \mathrm{~N}$ where the value of x is $\_\_\_\_$
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Solution
$ \begin{aligned} &\text { Thermal force } F=A y \propto \Delta T\\ &\begin{aligned} & \mathrm{F}=\left(10 \times 10^{-4}\right)\left(2 \times 10^{11}\right)\left(10^{-4}\right)(400) \\ & \mathrm{F}=8 \times 10^5 \mathrm{~N} \\ & \Rightarrow \mathrm{x}=8 \end{aligned} \end{aligned} $$
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