A metal rod $2 \mathrm{~m}$ long increases in length by $1.6 \mathrm{~mm}$, when heated from $0^{\circ}…
A metal rod $2 \mathrm{~m}$ long increases in length by $1.6 \mathrm{~mm}$, when heated from $0^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$. The coefficient of linear expansion of metal rod is
$1.33 \times 10^{-5} /{ }^{\circ} \mathrm{C}$
$1.66 \times 10^{-5} /{ }^{\circ} \mathrm{C}$
$1.33 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
$1.66 \times 10^{-3} /{ }^{\circ} \mathrm{C}$
Solution
We know,
Coefficient of Linear expansion $\alpha=\frac{\mathrm{L}_2-\mathrm{L}_1}{\mathrm{~L}_1 \Delta \mathrm{T}}... (i)$
Given: $\Delta \mathrm{T}=60-0=60^{\circ} \mathrm{C}$
$\mathrm{L}_1=2 \mathrm{~m}$ and $\mathrm{L}_2=2.0016$
Substituting the given values into (i),
$\alpha=\frac{.0016}{120}=1.33 \times 10^{-5} /{ }^{\circ} \mathrm{C}$