A surveyor’s steel tape 30 m long has a cross-section of 15 mm × 0·75 mm. With this, line AB is measured as 150 m. If the force applied during measurement is 120 N more than the force applied at the time of calibration, what is the actual length of the line ? (Take the modulus of elasticity for steel as 200 kN/mm²)
- A149·992 m
- B150·008 mCorrect
- C151·016 m
- D148·008 m
Solution
Concept
Pull correction
Formula
Cp = (P − P₀) L / (A E)
Step-by-step solution
1. A = 15 × 0.75 = 11.25 mm²; E = 200 000 N/mm². 2. Elongation per tape length = 120 × 30 000 / (11.25 × 200 000) = 1.6 mm. 3. The tape becomes 30.0016 m long, so the true length of the line = 150 × 30.0016 / 30 = 150.008 m.
Explanation
The extra pull stretches the tape, so each 'tape length' covers more ground than 30 m. The measured length is therefore less than the true length and the correction is positive.
Why the other options are wrong
149.992 m has the wrong sign. 151.016 and 148.008 are far too large for a 1.6 mm stretch per tape.
Shortcut
Tape too long → add correction: +1.6 mm per 30 m.
Common mistake
Subtracting the pull correction.
Correct answer: B) 150·008 m