Question

An iron bar $10cm$ in length is kept at $20{}^{\circ }C$ . If the coefficient of linear expansion of iron is $\alpha =11\times 10^{-6}{}^{\circ }{C}^{-1}$ , then at $19{}^{\circ }C$ it will be

• A. $11\times 10^{-6}cm$ longer
• B. $11\times 10^{-6}cm$ shorter
• C. $11\times 10^{-5}cm$ shorter
• D. $11\times 10^{-5}cm$ longer

Answer 1

Answer: (C)

$L=L_0\left(1+\alpha \Delta \theta \right)$
$\Rightarrow \frac{L_1}{L_2}=\frac{1+\alpha {\left(\Delta \theta \right)}_1}{1+\alpha {\left(\Delta \theta \right)}_2}$
$\Rightarrow \frac{10}{L_2}=\frac{1+11\times 10^{-6}\times 20}{1+11\times 10^{-6}\times 19}$
$\Rightarrow L_2=9.99989$
$\Rightarrow$ Length is shorten by
$10-9.99989=0.00011=11\times 10^{-5}cm$