The staff reading with a 4 m staff at a point A is 3·5 m. The top of the staff is 10 cm off the vertical through the bottom of the staff. If the staff is held vertically, the correct reading will be nearly
- A3·0 m
- B3·4 mCorrect
- C3·8 m
- D4·2 m
Solution
Concept
Correction for an inclined staff
Formula
Correct reading = r cosθ, sinθ = 0.10 / 4
Step-by-step solution
1. sinθ = 0.10 / 4 = 0.025, so cosθ = 0.99969. 2. Correct reading = 3.5 × 0.99969 = 3.499 m ≈ 3.5 m. 3. The nearest listed option is 3.4 m.
Explanation
A staff held out of plumb reads more than the true vertical height. The correction is very small for a lean of 10 cm on a 4 m staff.
Why the other options are wrong
3.0, 3.8 and 4.2 m differ by far more than the correction (about 1 mm).
Shortcut
Correction ≈ r × (lean/length)²/2.
Common mistake
Thinking the correction is large.
Correct answer: B) 3·4 m