Question

What is the percentage change in length of $1m$ iron rod if the temperature change by ${100}^{\circ }C$ (Assume coefficient of linear expansion, $\alpha =2\times {10}^{-5}{}^{\circ }{C}^{-1}$)

• A. $0.1\%$
• B. $0.2\%$
• C. $0.3\%$
• D. $0.4\%$

Answer 1

The correct option is B

$0.2\%$

Given:
Length of rod, $l=1m$ and change in temperature, $\Delta T={100}^{\circ }C$
Coefficient of linear expansion of iron rod, $\alpha =2\times {10}^{-5}{}^{\circ }{C}^{-1}$
Now,
$l_1=l(1+\alpha \Delta T)$
where, $l_1$ is the final length of the iron rod, $l$ is the original length of the iron rod, $\alpha$ is the coefficient of linear expansion of iron rod and $\Delta T$ is the change in temperature of iron rod.
or, $l_1-l=l\times \alpha \times \Delta T$
or, $\frac{\Delta l}{l}=\alpha \Delta T=2\times {10}^{-5}\times 100$
or, $\frac{\Delta l}{l}=2\times {10}^{-3}$
Therefore, % change in length $=\frac{\Delta l}{l}\times 100=2\times {10}^{-3}\times 100=0.2\%$