During levelling across a river, surveyor adopted reciprocal meth

During levelling across a river, surveyor adopted reciprocal meth
| During levelling across a river, surveyor adopted reciprocal method to minimize the error, due to wider width of the river. While he set up the instrument on one side of the bank, the readings on the staff held near and on the opposite bank of instruments was 1.237 m and 1.010 m respectively. Now, when the instrument was set up at the opposite bank, the readings on the staff held near and on the opposite bank of instruments observed was 1.900 m and 2.330 m respectively. Find the true elevation difference (in meters) between the two banks of the river.

A. 0.23

B. 0.33

C. 0.43

D. 0.53

Please scroll down to see the correct answer and solution guide.

Right Answer is: B

SOLUTION

Concept:

For reciprocal levelling:

True levelling (h) \(= \frac{1}{2}\left[ {({{\rm{n}}_{\rm{a}}} - {{\rm{f}}_{\rm{a}}}} \right) + \left( {{{\rm{f}}_{\rm{b}}} - {{\rm{n}}_{\rm{b}}}} \right)]\)

True error (e) \(= \frac{1}{2}\left[ {({{\rm{n}}_{\rm{a}}} - {{\rm{f}}_{\rm{a}}}} \right) - \left( {{{\rm{f}}_{\rm{b}}} - {{\rm{n}}_{\rm{b}}}} \right)]\)

Calculation:

Given:

When the instrument was held at one of the banks:

Reading on staff at A (na) = 1.237 m

Reading on staff at B (fa) = 1.01 m

When the instrument was held on the opposite banks:

Reading on staff at A (fb) = 2.33 m

Reading on staff at B (nb) = 1.9 m

True difference in elevation b/w A & B (h) is given by:

\({\rm{h}} = \frac{1}{2}\left[ {({{\rm{n}}_{\rm{a}}} - {{\rm{f}}_{\rm{a}}}} \right) + \left( {{{\rm{f}}_{\rm{b}}} - {{\rm{n}}_{\rm{b}}}} \right)\left] { = \frac{1}{2}} \right[\left( {1.237 - 1.01} \right) + \left( {2.33 - 1.9} \right) = 0.3285\;{\rm{m}}\) 

Related Questions