Question:
A steel rod with $\mathrm{y}=2.0 \times 10^{11} \mathrm{Nm}^{-2}$ and $\alpha=10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ of length $4 \mathrm{~m}$ 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 $x \times 10^{5} \mathrm{~N}$ where the value of $\mathrm{x}$ is .............
Solution:
Thermal force $F=A y \propto \Delta T$
$\mathrm{F}=\left(10 \times 10^{-4}\right)\left(2 \times 10^{11}\right)\left(10^{-5}\right)(400)$
$\mathrm{F}=8 \times 10^{5} \mathrm{~N}$
$\Rightarrow x=8$