A tape of standard length 20 m at 85°F was used to measure a base line. The measured distance was 882·50 m. What is the true length of the line, if the mean temperature during measurement was 63°F and the coefficient of thermal expansion of the tape material is 6·5 × 10⁻⁶ per °F ?
- A872·982 m
- B879·282 m
- C882·374 mCorrect
- D882·626 m
Solution
Concept
Temperature correction
Formula
Ct = α (Tm − T₀) L
Step-by-step solution
1. Ct = 6.5×10⁻⁶ × (63 − 85) × 882.50 = −0.1262 m. 2. The tape is shorter than its standard length at 63°F, so it records more than the true length: true length = 882.50 − 0.126 = 882.374 m.
Explanation
Below the standard temperature the tape contracts, so each tape length is shorter than 20 m and the measured distance is too large; the correction is negative.
Why the other options are wrong
882.626 m has the wrong sign. 872.982 m and 879.282 m are far too large corrections.
Shortcut
Temperature below standard → correction negative.
Common mistake
Adding the correction.
Correct answer: C) 882·374 m