Question

An iron bar $10 \, cm$ 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)

$L=L_{0}\left(1 + \alpha \Delta \theta \right)$
$\Rightarrow \, \, \frac{L_{1}}{L_{2}}=\frac{1 + \alpha \left(\Delta \theta \right)_{1}}{1 + \alpha \left(\Delta \theta \right)_{2}}$
$\Rightarrow \, \, \, \frac{10}{L_{2}}=\frac{1 + 11 \times 1 0^{- 6} \times 20}{1 + 11 \times 1 0^{- 6} \times 19}$
$\Rightarrow \, \, L_{2}=9.99989$
$\Rightarrow $ Length is shorten by
$10-9.99989=0.00011=11\times 10^{- 5} \, cm$