A steel rod of length 1m is heated from 25°C to 75°C keeping its length constant. The longitudinal strain developed in the rod is (Given: Coefficient of linear expansion of steel = 12 x ${10}^{-6}{/}^0\mathrm{C}$)

Due to the Expansion of the rod due to heating it, the rod develops a strain, trying to resist the change in length. Thus the strain tends to reduce the length of the rod.

$\mathrm{Strain} \Rightarrow \frac{∆\mathrm{L}}{\mathrm{L}} = \frac{\mathrm{L\alpha }∆\mathrm{\theta }}{\mathrm{L}} \Rightarrow \mathrm{\alpha }∆\mathrm{\theta }$

Strain $\Rightarrow -12 \times {10}^{-6}\times 50$

$\Rightarrow -6\times {10}^{-4}$