# Surveying Questions and Answers – Theodolite Traversing – Closing Error and its Limitation

This set of Surveying Multiple Choice Questions & Answers (MCQs) focuses on “Theodolite Traversing – Closing Error and its Limitation”.

1. In order to mitigate the closing error, sum of latitudes and departures must be equal to zero.
a) True
b) False

Explanation: The algebraic sum latitudes and algebraic sum of departures must be equal to zero for avoiding the closing error, which will occur when the end point don’t coincide with the starting point.

2. Which among the following determines the direction of closing error?
a) Tan δ = ∑L/∑D
b) Tan δ = ∑L2/∑D2
c) Tan δ = ∑D/∑L
d) Tan δ = ∑D2/∑L2

Explanation: From the figure, Tan δ =∑D/∑L, which will give the direction of the closing error.

3. The sum of interior angles must be equal to_______
a) (2N+4) right angles
b) (2N-4) right angles
c) (2N+4) * 180
d) (2N-4) * 180

Explanation: The theoretical sum of the interior angles of a traverse should equal to (2N-4) right angles, and that of the exterior angles should equal to (2N+4) right angles, where N is the number of sides of a closed traverse.

4. For adjusting the angular error, the error may be distributed equally among all the angles.
a) False
b) True

Explanation: When all angles are measured and under similar conditions, angular error is distributed equally among all the angles. However, if the accuracy of some angle is suspected due to peculiar field conditions, the whole angular error may be assigned to that angle.

5. Closing error can be given as________
a) ((∑L)2+(∑D)2)1/4
b) (∑L2-∑D2)1/2
c) (∑L2*∑D2)1/2
d) ((∑L)2+(∑D)2)1/2

Explanation: If a closed traverse is plotted according to the field measurements, the end point of the traverse will not coincide exactly with the starting point, due to the errors in the field observations, such as error is known as closing error. This is given as,
Closing error, e =  ((∑L)2+(∑D)2)1/2
Where, ∑L = sum of latitudes, ∑D = sum of departures.

6. Which of the following corresponds to the correction applied to the bearing of the last side?
a) Correction = Ne/N
b) Correction = 2Ne/N
c) Correction = 3Ne/N
d) Correction = e/N

Explanation: If e is the closing error in bearing, and N is the number of the sides of the traverse, then the correction applied to the bearing of the sides will be
Correction to the first bearing = e/N
Correction to the first bearing = 2e/N
And so on to the last bearing = Ne/N = e.

7. If traversing is done by taking bearings of the lines, the closing error in bearing may be determined by _______________
a) Comparing the back and fore bearings of the last line of the open traverse
b) Comparing the back and fore bearings of the middle line of the closed traverse
c) Comparing the back and fore bearings of the last line of the closed traverse
d) Comparing the back and fore bearings of the first line of the closed traverse

Explanation: By comparing the back and fore bearings of the last line of the closed traverse, the error in bearing may be determined by finding the difference between its observed bearing and known bearing.

8. Which of the following is a method of adjusting a closed traverse?
a) Departure method
b) Axis method
c) Tangential method
d) Latitude method

Explanation: The methods which are used to adjust the traverse are Bowditch’s rule, Transit rule, Axis method and Graphical method. These are employed based on the precision of the values obtained during surveying.

9. Relative error of closure is given as____________
a) Perimeter of closure/error of traverse
b) Error of perimeter/perimeter of traverse
c) Perimeter of traverse/error of traverse
d) Error of closure/perimeter of traverse

Explanation: The relative error of closure is used only in case of determination of the sign of latitudes and departures i.e., in which quadrant latitudes and departures lie.

10. Closing error can be briefly explained in which of the following set of methods?
a) Bowditch’s, Transit methods
b) Transit, Axis methods
c) Graphical, Axis methods
d) Bowditch’s, Graphical methods

Explanation: Since more amount of diagrammatic explanation is involved in Graphical and Axis methods, those are able to explain in a brief manner.

11. From the following observations, calculate closing error.

Line Length (m) Latitude Departure
AB 92.96 +92.57 -217.92
BC 157.63 -317.39 +24.62
CA 131.24 +226.19 +192.36

a) 1.66
b) 1.55
c) 1.44
d) 1.99

Explanation: The value of closing error can be given by e =  ((∑L)2+(∑D)2)1/2
Where, ∑L = 92.57 – 317.39 + 226.19 = 1.37
∑D = -217.92 + 24.62 + 192.36 = – 0.94
On substituting, we get e =  ((∑L)2+(∑D)2)1/2
e = (1.372+ 0.942)1/2
e = 1.661.

12. Calculate the direction of closing error for the following data.

Line Length (m) Latitude Departure
AB 24.29 -102.31 -119.22
BC 130.32 +360.24 -204.92
CA 249.11 -257.43 +323.26

a) 50023ꞌ
b) 60029ꞌ
c) 60023ꞌ
d) 62023ꞌ

Explanation: The value of direction for closing error can be given as Tan δ =∑D/∑L, where ∑L = – 102.31 + 360.24 –257.43 = 0.5; ∑D = -119.22 – 204.92 + 323.26 = -0.88. On substitution we get, Tan δ = 0.88 / 0.5 = 60023ꞌ.

13. For a traverse containing 10 sides, what would be the correction applied for the first side, if it consists a closing error of +1.92?
a) 19.0
b) 19.2
c) 1.902
d) 0.192

Explanation: The correction for sides in a traverse is given as correction = e / N, where N is the number of sides and e is the closing error. On substitution, we get, correction = 1.92 / 10 = 0.192.

14. What would be the correction for any side of a traverse in axis method if it has a closing error e = 0.93, length of side and axis would be 243.13 and 100 respectively?
a) 2.131
b) 1.131
c) 1.113
d) 1.311

Explanation: In Axis method of balancing a traverse, correction = length of side * (e/2) / length of axis. On substitution we get,
Correction = 243.13 * (0.93/2) / 100 = 1.131.

15. Which of the following indicates the correct value of precise closing error if e = 0.54 and lengths of sides are 92.69 m, 119.23 m, 92.64 m, 42.96 m and 60.96 m.
a) 1 / 766.445
b) 1 / 746.445
c) 1 / 756.445
d) 1 / 765.445

Explanation: The precise error of closure can be given as, error of closure = e / p
Where e = closing error = 0.54 and p = perimeter of traverse = 92.69 + 119.23 + 92.64 + 42.96 + 60.96 = 408.48 m.
Precise error is given as 0.54 / 408.48 = 1 / 756.445.

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