A steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 imes 10^{-5} \mathrm{~m}$ at a certain temperature. The maximum temperature variation allowable during the ruling is (Coefficient of linear expansion of steel $=10 imes 10^{-6} \mathrm{~K}^{-1}$ )

Question

A steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 	imes 10^{-5} \mathrm{~m}$ at a certain temperature. The maximum temperature variation allowable during the ruling is (Coefficient of linear expansion of steel $=10 	imes 10^{-6} \mathrm{~K}^{-1}$ )

Aicharya · Accepted Answer

Change in length $\Delta L=5 	imes 10^{-5} \mathrm{~m}$ Initial length $L=1 \mathrm{~m}$ $\alpha=10 	imes 10^{-6} /{ }^{\circ} \mathrm{C}$ $	herefore$ Change in temperature $\begin{aligned} \Delta t & =\frac{\Delta L}{\alpha L}=\frac{5 	imes 10^{-5}}{10 	imes 10^{-6} 	imes 1} \ & =5^{\circ} \mathrm{C}\end{aligned}$

A steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5}…

Solution