Question

An iron bar of length $10m$ is heated from $0^{°}C$ to $100^{°}C$ . If the coefficient of linear thermal expansion of iron is $10\times 10^{-6}{/}^{°}C$ , the increase in the length of bar is :

• A. $0.5cm$
• B. $1.0cm$
• C. $1.5cm$
• D. $2.0cm$

Answer 1

Answer: (B)

The change in length $\Delta l$ is proportional to $L$ and $\Delta T$. Stated mathematically
$\Delta l=\alpha L\Delta T$
where $\alpha$ is called the coefficient of linear thermal expansion for the material.
Given, $\alpha =10\times 10^{-6}/{}^{\circ }C,\Delta T=100^{\circ }C$
$L=10m$
$\therefore \Delta l=10\times 100\times 10\times 10^{-6}=10^{-2}m=1cm$