Question

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

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

Answer 1

Answer: (C)

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

Given,

$l=1m$

$T_1={25}^{0}C$

$T_2={75}^{0}C$

$\alpha =12\times {10}^{-6}degreeC$

$\Delta T=T_2-T_1={75}^{0}C-{25}^{0}C={50}^{0}C$

Strain$=-\frac{\Delta l}{l}=-\frac{l\alpha \Delta T}{l}=-\alpha \Delta T$

$Strain=-6\times {10}^{-6}\times 50$

$Strain=-6\times {10}^{-4}$

The correct option is C.