Question

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

• A. $26.00468m$
• B. $25.90201m$
• C. $26.35048m$
• D. $26m$ (should not change)

Answer 1

The correct option is A

$26.00468m$

Let the temperature rise above the correct temperature be $\theta$.

$\Rightarrow$$\theta$ = ${35}^{\circ }C-{20}^{\circ }C$ = ${15}^{\circ }C$.

Using the relation, correct length = measured length ($1+\alpha \theta$),

true distance between the points -

= $26(1+1.2\times {10}^{-5}\times 15)$

$\Rightarrow$ true distance = $26.00468m$.