Question

A surveyor’s $30m$ steel tape is correct at $68{}^{\circ }C$. On a hot day the tape has expanded to $30.01m$. On that day, the tape indicates a distance of $15.52m$ between two points. The true distance between these points is

• A. $15.50m$
• B. $15.51m$
• C. $15.52m$
• D. $15.53m$

Answer 1

The correct option is B

$15.51m$

Step 1: Given Data

1. The Temperature at which steel tape is correct is $68{}^{\circ }C$
2. The true Length of the steel tape is $30m$
3. On a hot day, the new length of the steel tape is $30.01m$
4. Measured distance by the incorrect steel tape is $15.52m$

Step 2: The calculation for True Distance

As the new length (extended length) of the tape is $30.01m$

Therefore, the error is of $\left(30.01m-30m=0.01m\right)$ will incurred.

Hence, the distance between points is less but the tape will indicate $0.01m$more.

Similarly, if the tape indicates $15.52m$as its true length, then the actual length would be $\left(15.52\text{-}0.01m=15.51m\right)$

Hence option (B) $15.51m$ is the correct answer