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Question

A surveyor’s 30 m steel tape is correct at a temperature of 20°C. The distance between two points, as measured by this tape on a day when the temperature is 35°C, is 26 m. What is the true distance between the points?$\left({\mathrm{\alpha}}_{\text{steel}}=1.2\times {10}^{-5}{/}^{\circ}\mathrm{C}\right)$

Easy

Solution

Let temperature above the correct temperature be

$\Rightarrow \phantom{\rule{1em}{0ex}}\theta =35-20={15}^{\circ}\mathrm{C}$ (Using the relation)

Correct length = measured length$(1+\mathrm{\alpha \theta})$

True distance between the points = 26(1+ 1.2 x10^{-5} X1.5)

$\Rightarrow \phantom{\rule{1em}{0ex}}\text{True distance}=26.00476\mathrm{m}$

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The coefficient of linear expansion of brass and steel are ${\mathrm{\alpha}}_{1}$ and ${\alpha}_{2}$. If we take a brass rod of length ${l}_{1}$ and steel rod of length ${l}_{\mathit{2}}$ at 0^{o}C, their difference in length $\left({l}_{2}-{l}_{1}\right)$will remain the same at all temperatures if

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