Question

What will be the increase in length of a steel rod of length $0.5m$, when its temperature is increased by ${60}^{\circ }C$? The coefficient of linear expansion of steel is $0.000013{}^{\circ }{C}^{-1}$.

• A. $0.019cm$
• B. $0.045cm$
• C. $0.015cm$
• D. $0.039cm$

Answer 1

The correct option is D $0.039cm$

Given, initial length of the rod, $l_1=0.5m$, change in temperature, $\Delta T={60}^{\circ }C$, and coefficient of linear expansion, $\alpha =0.000013{}^{\circ }{C}^{-1}$
Let change in length be $\Delta l$
Using the relation,
$\Delta l=\alpha \times l_1\times \Delta T$ $=0.000013\times 0.5\times 60$ $=0.00039m=0.039cm$
Therefore, increase in length is $0.039cm$