Question

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

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

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=10 \,m $
$\therefore \, \Delta\,l=10 \times 100 \times 10 \times 10^{-6}=10^{-2} \,m =1\, cm$