Question

A survey line was measured to be 285.5 m with a tape having a nominal length of 30 m. On checking, the true length of the tape was found to be 0.05 m too short. If the line lay on a slope of 1 in 10, the reduced length (horizontal length) of the line for plotting of survey work would be

• A. 285.6 m
• B. 283.6 m
• C. 285.0 m
• D. 284.5 m

Answer 1

The correct option is B 283.6 m

Measured length = 285.5 m
Nominal length of tape = 30 m
Slope = 1 in 10
The tape is 0.05 m too short
Actual length of tape = 30-0.05=29.95 m
Actual length measured

$=\frac{\text{Actual length of tape}}{\text{Nominal length of tape}}\times \text{Measured length}$

$=\frac{29.95}{30}\times 285.5=285.024m$

$Nowslopecorrection=\frac{-h^2}{2L}$

$\because Slope=1in10$

$\Rightarrow h=\frac{1}{10}\times 285.024$

$\Rightarrow h=28.5024m$

$\Rightarrow Slopecorrection=\frac{-(28.5024{)}^2}{2\times 285.024}$


= -1.42512m

$\Rightarrow Lengthtobeplotted=Actuallengthmeasured+correction$

=285.024 + (-1.42512)

=283.599 m

Hence, option (d) is correct.