This set of Surveying Multiple Choice Questions & Answers (MCQs) focuses on “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

View Answer

Explanation: Mid-ordinate calculation involves the following procedure,

O

_{0}= R – (R

^{2}– (l/2)

^{2})

^{1/2}. On substitution, we get

O

_{0}= 40.62 – (40.62

^{2}– (10.2/2)

^{2})

^{1/2}

O

_{0}= 0.33.

2. For setting the curve, chord must be divided into even number of equal parts.

a) True

b) False

View Answer

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) O_{x} = (R^{2} + (x)^{2})^{1/2} – (R – O_{0})

b) O_{x} = (R^{2} – (x)^{2})^{1/2} – (R – O_{0})

c) O_{x} = (R^{2} – (x)^{2})^{1/2} + (R – O_{0})

d) O_{x} = (R^{2} – (x)^{2})^{1/2} – (R + O_{0})

View Answer

Explanation: The formula for setting a long chord by using ordinate can be given as O

_{x}= (R

^{2}– (x)

^{2})

^{1/2}– (R – O

_{0}). In this O

_{0}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

View Answer

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

View Answer

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.

6. Which of the following indicates the formula for determining ordinate in an approximate method?

a) O_{x} = x*(l-x) / 2+R

b) O_{x} = x*(l-x) / 2*R

c) O_{x} = x*(l + x) / 2*R

d) O_{x} = x+ (l-x) / 2*R

View Answer

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 O

_{x}= 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

View Answer

Explanation: The value of ordinate placed at certain distance x can be found out by using the formula,

O

_{x}= (R

^{2}– (x)

^{2})

^{1/2}– (R – O

_{0}). On substitution, we get

O

_{x}= (22.92

^{2}-(10)

^{2})

^{1/2}– (22.92 – 12.12)

O

_{x}= 9.823.

8. If the value of O_{0} = 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

View Answer

Explanation: The general method of the ordinate calculation involves,

O

_{0}= R – (R

^{2}– (l/2)

^{2})

^{1/2}. On substitution, we get

24.62 = 4 – (4

^{2}– (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) \( R – (R^2 – (\frac{l}{2})^2)^{1/2}\)

View Answer

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

View Answer

Explanation: Since the radius of the curve is large, we may consider the approximate method i.e.,

O

_{x}= x*(l-x) / 2*R. on substitution, we get

O

_{x}= 20*(42.92-20) / 2*72.46

O

_{x}= 3.16.

**Sanfoundry Global Education & Learning Series – Surveying.**

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