# Surveying Questions and Answers – Curve Surveying – By Ordinates of the Long Chord

This set of Surveying Multiple Choice Questions & Answers (MCQs) focuses on “Curve Surveying – By Ordinates of the Long Chord”.

1. Find the value of mid-ordinate if the radius of the curve is given as 40.62 m and length as 10.2m.
a) 0.43
b) 0.22
c) 0.12
d) 0.33

Explanation: Mid-ordinate calculation involves the following procedure,
O0 = R – (R2 – (l/2)2)1/2. On substitution, we get
O0 = 40.62 – (40.622 – (10.2/2)2)1/2
O0 = 0.33.

2. For setting the curve, chord must be divided into even number of equal parts.
a) True
b) False

Explanation: While setting a curve, the chord must be divided into even number of equal parts in order to decrease the time of the entire process. After dividing, the offsets are calculated.

3. Which of the following indicates the formula for setting a long chord by using ordinate?
a) Ox = (R2 + (x)2)1/2 – (R – O0)
b) Ox = (R2 – (x)2)1/2 – (R – O0)
c) Ox = (R2 – (x)2)1/2 + (R – O0)
d) Ox = (R2 – (x)2)1/2 – (R + O0)

Explanation: The formula for setting a long chord by using ordinate can be given as Ox = (R2 – (x)2)1/2 – (R – O0). In this O0 is given as mid ordinate, R indicates the radius of the curve, x indicates the distance of the point from mid region.

4. General method can be adopted when radius of the curve is large.
a) False
b) True

Explanation: When the radius of the curve is large, general method might take more time while solving than expected. In order to reduce the time of procedure we generally adopt an approximate method which is only considered in case of large radius than the length of the chord.

5. In approximate method, the value of x is measured from ____________
a) Chord point
b) Mid point
c) Tangent point
d) Secant point

Explanation: In general, the value of x is taken from the midpoint but in case of approximate method the x value is taken from the tangent point. It is so because of the larger radius.
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6. Which of the following indicates the formula for determining ordinate in an approximate method?
a) Ox = x*(l-x) / 2+R
b) Ox = x*(l-x) / 2*R
c) Ox = x*(l + x) / 2*R
d) Ox = x+ (l-x) / 2*R

Explanation: When the radius of the curve is large, for decreasing the time period of the entire process this process is adopted. It involves calculation of ordinate by assuming perpendicular distance and the formula is given as Ox = x*(l-x) / 2*R.

7. Find the value of ordinate at a distance of 10m having radius of 22.92m with mid-ordinate12.12.
a) 3.289
b) 2.892
c) 8.293
d) 9.823

Explanation: The value of ordinate placed at certain distance x can be found out by using the formula,
Ox = (R2 – (x)2)1/2 – (R – O0). On substitution, we get
Ox = (22.922-(10)2)1/2 – (22.92 – 12.12)
Ox = 9.823.

8. If the value of O0 = 24.62 and R = 4m, find the value of l using the general method of long chords.
a) 1636.73m
b) 1363.73m
c) 1366.73m
d) 1363.37m

Explanation: The general method of the ordinate calculation involves,
O0 = R – (R2 – (l/2)2)1/2. On substitution, we get
24.62 = 4 – (42 – (l/2)2)1/2
l = 1636.73 m.

9. Which of the following indicates the formula for a general method by ordinate of long chords?
a) $$R + (R^2 – (\frac{l}{2})^2)^{1/2}$$
b) $$R * (R^2 – (\frac{l}{2})^2)^{1/2}$$
c) $$R – (R^2 + (\frac{l}{2})^2)^{1/2}$$
d) $$R – (R^2 – (\frac{l}{2})^2)^{1/2}$$

Explanation: The perpendicular which is erected while setting curve by ordinates of long chords, is equal to versed sine of the curve which makes it equal to $$R – (R^2 – (\frac{l}{2})^2)^{1/2}$$.

10. What will be value of ordinate placed at a distance of 20m having radius and length as 72.46m and 42.92m respectively?(use approximate method)
a) 6.13
b) 1.36
c) 3.16
d) 4.86

Explanation: Since the radius of the curve is large, we may consider the approximate method i.e.,
Ox = x*(l-x) / 2*R. On substitution, we get
Ox = 20*(42.92-20) / 2*72.46
Ox = 3.16.

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