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A steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5} \mathrm{~m}$ at a certain temperature. The maximum temperature variation allowable during the ruling is
(Coefficient of linear expansion of steel $=10 \times 10^{-6} \mathrm{~K}^{-1}$ )
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(Coefficient of linear expansion of steel $=10 \times 10^{-6} \mathrm{~K}^{-1}$ )
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The correct answer is:
$5^{\circ} \mathrm{C}$
Change in length $\Delta L=5 \times 10^{-5} \mathrm{~m}$ Initial length $L=1 \mathrm{~m}$ $\alpha=10 \times 10^{-6} /{ }^{\circ} \mathrm{C}$
$\therefore$ Change in temperature
$\begin{aligned} \Delta t & =\frac{\Delta L}{\alpha L}=\frac{5 \times 10^{-5}}{10 \times 10^{-6} \times 1} \\ & =5^{\circ} \mathrm{C}\end{aligned}$
$\therefore$ Change in temperature
$\begin{aligned} \Delta t & =\frac{\Delta L}{\alpha L}=\frac{5 \times 10^{-5}}{10 \times 10^{-6} \times 1} \\ & =5^{\circ} \mathrm{C}\end{aligned}$
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