Correct Answer: D. 13.3
Solution:
The specified accuracy is an error of 1 cm for every 60 m of length.
Error per meter = (1 cm) / (60 m).
Total error for an 80 m offset = (1 cm / 60 m) × 80 m = 80/60 cm = 4/3 cm.
Converting to millimeters: (4/3) cm × 10 mm/cm ≈ 13.33 mm.
Correct Answer: C. 23.8
Solution:
The chain is too long, so the correction will be positive.
Designated length of chain (L) = 20 m.
Actual length of chain (L') = 20.2 m.
Error per chain length = L' - L = 20.2 - 20 = 0.2 m.
Number of chain lengths in the measurement = (Measured distance) / L = 2380 / 20 = 119.
Total correction = Number of chain lengths × Error per chain = 119 × 0.2 = 23.8 m.
Correct Answer: A. 19.9 m
Solution:
The formula relating true length, measured length, and chain lengths is:
True Length = (Actual Chain Length / Designated Chain Length) × Measured Length
398 = (L' / 20) × 400
L' = (398 × 20) / 400
L' = 19.9 m. The chain was shorter than its designated length.
Correct Answer: B. Invar tape > steel tape > metallic tape > linen tape
Solution:
The accuracy of measuring tapes primarily depends on their material's stability and resistance to environmental changes.
- Invar Tape: Most accurate, made of a nickel-steel alloy with a very low coefficient of thermal expansion.
- Steel Tape: Highly accurate, but affected by temperature changes.
- Metallic Tape: A cloth tape reinforced with metal wires to reduce stretching. Less accurate than steel.
- Linen Tape: Least accurate, as it is prone to stretching, shrinking with moisture, and wear.
Correct Answer: D. 30°
Solution:
In chain surveying, the framework consists of triangles. For accurate plotting, these triangles should be "well-conditioned." A well-conditioned triangle is one in which no angle is too small or too large. The standard guideline is that no angle should be less than 30° or greater than 120°. This ensures a sharp, well-defined intersection of the arcs when plotting the triangle's vertices.
Correct Answer: C. Tie line
Solution:
A Tie Line is a line that joins subsidiary or tie stations on the main survey lines. Its primary purpose is to take the details of interior features of the area which are far away from the main lines. It is also useful for checking the accuracy of the framework.
Correct Answer: B. Double reflection from two mirrors
Solution:
The optical square works on the principle of double reflection. It uses two mirrors placed at an angle of 45° to each other. A ray of light from an object is reflected by both mirrors, and the emergent ray is deviated by 90° from its original path. This allows the surveyor to set out a perfect right angle.
Correct Answer: A. h2 / (2ℓ)
Solution:
The slope correction is the difference between the length measured along the slope (ℓ) and the true horizontal distance. Using the Pythagorean theorem, the horizontal distance (H) is √(ℓ2 - h2). The correction (C) is ℓ - H. For small slopes, this can be approximated by the formula C ≈ h2 / (2ℓ), which is a very common formula used in chain surveying for slope correction.
Correct Answer: D. 101.6
Solution:
The relationship between true area and measured area is: True Area = Measured Area × (L'/L)2, where L' is the actual length of the chain and L is the designated length.
Assuming a standard Gunter's chain of 100 links.
L = 100 links.
L' = 100 + 0.8 = 100.8 links.
True Area = 100 acres × (100.8 / 100)2 = 100 × (1.008)2 ≈ 100 × 1.016064 ≈ 101.6 acres.
Correct Answer: A. 50α2
Solution:
The slope correction formula is C = L(1 - cos α). For a small angle α (in radians), cos α can be approximated by the Taylor series expansion: 1 - α2/2.
Substituting this in the formula: C ≈ L(1 - (1 - α2/2)) = L(α2/2).
Given the chain length L = 100 links, the correction is: C ≈ 100(α2/2) = 50α2.
Correct Answer: C. to indicate the accuracy of the survey work
Solution:
A Check Line (or proof line) is a line measured in the field to check the accuracy of the survey framework. The length of the check line as measured on the ground should agree with its length on the plotted plan. It is typically run between the apex of a triangle and some point on the opposite side.
Correct Answer: B. by left hand upright
Solution:
When setting out a perpendicular on the right side of the chain line, the surveyor holds the optical square upright with the left hand over the station point on the chain line. They then sight through the instrument towards the forward ranging rod and signal the assistant to move a ranging rod until its image, seen in the mirror, coincides with the forward rod's direct image.
Correct Answer: D. 50/n2
Solution:
A slope of 1 in n means tan(θ) = 1/n. For small angles, tan(θ) ≈ θ. So, the angle of slope θ ≈ 1/n radians. The slope correction (C) for a chain of length L is approximately C ≈ Lθ2/2.
Given L = 100 links and θ ≈ 1/n:
C ≈ 100 * (1/n)2 / 2 = 100 / (2n2) = 50/n2.
Note: Some sources use a different approximation, C ≈ L/(2n2), which would give 100/(2n2) if L=100. However, the most standard approximation leads to 50/n2.
Correct Answer: A. Always cumulative
Solution:
Slope correction accounts for the difference between the measured slope distance and the true horizontal distance. Since the sloped distance is always longer than the horizontal distance, the correction is always subtractive. Because it always has the same sign (negative), it is a cumulative error, meaning the error adds up over the length of the survey line.
Correct Answer: A. 3.75 cm
Solution:
For a gradient of 1 in 'n', the slope correction (C) for a measured length (L) can be approximated by the formula C ≈ L / (2n2).
Here, L = 30 m and n = 20.
C ≈ 30 / (2 × 202) = 30 / (2 × 400) = 30 / 800 = 0.0375 m.
To convert the correction to centimeters, multiply by 100:
Correction = 0.0375 m × 100 cm/m = 3.75 cm.