A steel rod of length $1\,m$ and area of cross section $1\,cm^2$ is heated from $0\,^oC$ to $200\,^oC$ without being allowed to extend or bend. Find the tension produced in the rod $(Y = 2.0 \times 10^{11}\,Nm^{-2}$, $\alpha = 10^{-5} C^{-1})$
A steel rod of length $1\,m$ and area of cross section $1\,cm^2$ is heated from $0\,^oC$ to $200\,^oC$ without being allowed to extend or bend. Find the tension produced in the rod $(Y = 2.0 \times 10^{11}\,Nm^{-2}$, $\alpha = 10^{-5} C^{-1})$
Rise in temperature $\Delta t=200^{\circ} \mathrm{C}-0^{\circ} \mathrm{C}=200^{\circ} \mathrm{C}$
Tension produced in the rod,
$F=\mathrm{YA} \alpha \Delta t$
$=2 \times 10^{11} \times 1 \times 10^{-4} \times 10^{-5} \times 200$
$=4 \times 10^{4} \mathrm{~N}$
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