Question

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

• A. $6\times {10}^{-4}$
• B. $-6\times {10}^{-5}$
• C. $-6\times {10}^{-4}$
• D. zero

Answer 1

The correct option is C $-6\times {10}^{-4}$

Due to 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.

Strain $=\frac{\Delta L}{L}=\frac{L\alpha \Delta \theta }{L}=\alpha \Delta \theta$$=-12\times {10}^{-6}\times 50=-6\times {10}^{-4}$