Q. An iron bar of length 10m is heated from 0$℃$ to 100$℃$. If the coefficient of linear thermal expansion of iron is $10 \times 10^{- 6}℃^{- 1}$, the increase in the length of bar is
A) 0.5 cm
B) 1.0 cm
C) 1.5 cm
D) 2.0 cm
Explanation
(b) The change in length $\mathrm{\Delta}l$ is proportional to $l$ and $\mathrm{\Delta}T$. Stated mathematically
$\mathrm{\Delta}l = \alpha l\mathrm{\Delta}T$
Where $\alpha$ is called the coefficient of linear thermal expansion for the material.
Given, $\alpha = 10 \times 10^{- 6}/℃$ , $\mathrm{\Delta}T = 100℃$
$l = 10$m
$\ \ \therefore$ $\mathrm{\Delta}l = 10 \times 100 \times 10 \times 10^{- 6}$
= $10^{- 2}$m=1 cm
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.