This set of Surveying Multiple Choice Questions & Answers (MCQs) focuses on “Theodolite Traversing – Stadia Tacheometry”.

1. The value of multiplying constant is generally taken as _________
a) 60
b) 80
c) 90
d) 100

Explanation: In the expression k = 12*cot β2, the value of β is taken as 34022ꞌ64ꞌꞌ. On substituting the value of β in the equation, the value of k can be approximately equal to 100.

2. Stadia method can also be known as __________
a) Fixed hair method
b) Movable hair method
c) Subtense method
d) Tangential method

Explanation: Since the stadia wires are fixed, this method is known as Fixed hair method. The stadia hair can be moved in case of Movable hair method which is also known as subtense method. In tangential method horizontal and vertical distances can be measured by the instrument which consists only vane.

3. Which among the following represents stadia interval factor?
a) f + d
b) f – d
c) f / i
d) i/ f

Explanation: The horizontal distance between the axis and the staff can be given as
D = (f/i)*s + (f+d)
D = K*s + C
Where K is the stadia interval factor (or) the multiplying constant and C is the additive constant.

4. What is the formula for finding vertical distance if the staff is held vertical and line of sight is inclined?
a) V = Ks $$\frac{sin2θ}{2}$$ + C sin θ
b) V = Ks cos2 θ + C cos θ
c) V = Cs $$\frac{sin2θ}{2}$$ + K cos θ
d) V = Ks sin22 θ + C cos θ

Explanation: If the line of sight is inclined, the vertical distance calculated will include the values of sin which is derived from the horizontal distance formula i.e., V = Ks $$\frac{sin2θ}{2}$$ + C sin θ.

5. The value of additive constant lies in the range of__________
a) 0.2 to 0.3m
b) 0.3 to 0.45m
c) 0.5 to 0.6m
d) 0.6 to 0.7m

Explanation: Since the lens is provided in the internal focussing telescope, it reduces the value of the additive constant to a minimal range.

6. Usage of anallactic lens makes the entire process more simple and reliable.
a) True
b) False

Explanation: Due to the absorption of more amount of incident light, the anallactic lens makes the entire process simple and reliable. But the lens is adjustable, which may be a
cause for potential errors.

7. A tacheometer is setup at A and the readings on the staff at B are 1.77m, 2.12m, 2.34m and the inclination of line of sight is + 10 9ꞌ. Calculate the vertical distance between A and B. Take k = 100, c = 0.3?
a) 1.51 m
b) 2.51 m
c) 2.15 m
d) 1.15 m

Explanation: We know that the vertical distance can be computed by using
V = k s $$\frac{sin2θ}{2}$$ + c sin θ
S = 2.34 – 1.77 = 0.57m
On substitution,
V = (100*0.57*sin(2*109ꞌ))/2 + (0.3*sin(109ꞌ))
V = 1.15m.

8. What is the value of additive constant in anallactic lens?
a) 100
b) 0.3
c) 0
d) 0.4

Explanation: If the anallactic lens has been provided in the internal focussing telescope, the additive constant can be reduced to minimal value i.e., zero due to which the computations can be make quicker.

9. From the figure, the R.L of B can be____________

a) R.L of B = R.L of B.M + H.I + X + V
b) R.L = R.L of B.M + H.I + V – X
c) R.L = R.L of B.M + V – X
d) R.L = R.L of B.M + V + X

Explanation: The R.L of B can be obtained by calculating the value of vertical distance and by substituting in the formula R.L = R.L of B.M + H.I + X + V.

10. Subtense method is one of the classifications of stadia system.
a) True
b) False

Explanation: Stadia system is classified into movable hair method and fixed hair method in which, the movable hair method can also be known as sub tense method.

11. Calculate the value of K and C, if the measurements are taken between two points of 50 and 130 distant apart and the stadia readings will be 0.024, 0.824 respectively.
a) 0, 47.6
b) 47.6, 100
c) 100, 47.6
d) 47.6, 0

Explanation: We know that, D = Ks + C, on substituting the values of D, s, C we get two equations. 50 = k(0.024) + C; 130 = k(0.824) + C. On subtracting, we get
80 = k(0.8). We get, K = 100. Now, substitute this value in any of the equations to get the value of C. It can be given as 50 = 100*0.024 + C, C = 47.6.

12. The following are the staff readings given when the staff is held normal. The line of sight of instrument is placed at an angle +3024ꞌ. It being an anallactic lens, find the horizontal distance between staff and instrument station. Staff readings – 2.145 m, 1.925 m, 1.464 m.
a) 62.082 m
b) 58.082 m
c) 60.082 m
d) 68.082 m

Explanation: When the staff is placed normal, the value of horizontal distance can be given as D = (Ks + C) cos θ + r sin θ on substituting the values of s = 2.145 – 1.464 = 0.681, r = 1.925, θ, C = 0, we get,
D = 100*0.681* cos 3024ꞌ + 0 + 1.925* sin 3024ꞌ
D = 68.082 m.

13. Calculate the value of R.L for staff being vertical and possessing staff readings as follows 2.892, 2.234, 1.926. It being an anallactic lens possesses an instrumental height of 1.94 with R.L 102.34 m. Line of sight placed at an angle of 2042ꞌ.
a) 106.591 m
b) 105.591 m
c) 109.951 m
d) 100.981 m

Explanation: The R.L of the staff can be given as R.L = R.L of instrument station + H.I + v – r. the value of v can be calculated as v = k*s/2*sin2θ + c sin θ. On substitution we get,
V = 100 * (2.892-1.926)/2* sin (2*2042ꞌ) + 0
V = 4.545 m. R.L of staff is given as R.L = 102.34 + 1.94 + 4.545 – 2.234 = 106.591 m.