Question

For a dumpy level, the bubble tube has sensitivity of 40" for one division. While taking a staff reading at a distance of 60 m, the bubble is out of centre by 2 divisions. The error in staff reading in mm is \(\underline{\hspace{1cm}}\). (round off to one decimal place)

Hint:

For a dumpy level, errors caused by the bubble tube are proportional to the sensitivity and the distance.

Answer 1

Correct Answer: 22.5

The sensitivity of the bubble tube is given as 40" per division. The total error is:
\[ \text{Total error} = 40" \times 2 = 80" \] Convert angle in seconds to mm:
\[ 1" = \frac{1}{3600} \, \text{degree}, \text{Error in length} = 60 \times \tan(80") \] Approximation:
\[ \tan(80") \approx 0.02332 \] Thus, error in length:
\[ \text{Error} = 60 \times 0.02332 \approx 1.4 \, \text{mm} \] Thus, the error in staff reading is \( \boxed{1.4} \, \text{mm} \).