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Question

A surveyor's 30m steel tape is correct at a temperature of 20C. The distance between two points, as measured by this tape on a day when the temperature is 35C, is 26m. What is the true distance between the points? (αsteel = 1.2 × 105/C.)

A

26.00468 m

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B
25.90201 m
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C
26.35048 m
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D

26 m (should not change)

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Solution

The correct option is A

26.00468 m


Let the temperature rise above the correct temperature be θ.

θ = 35C20C = 15C.

Using the relation, correct length = measured length (1+αθ),

true distance between the points -

= 26 (1 + 1.2 × 105 × 15)

true distance = 26.00468 m.


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