# Surveying Questions and Answers – Curve Surveying – By Successive Bisection of Arcs or Chords

This set of Surveying written test Questions & Answers focuses on “Curve Surveying – By Successive Bisection of Arcs or Chords”.

1. Which of the following indicates the formula for linear method of bisection of arcs?
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 bisection of arcs, is equal to versed sine of the curve which makes it equal to $$R – (R^2 – (\frac{l}{2})^2)^{1/2}$$.

2. Find the perpendicular distance if the radius of the curve is given as 10.26m and the angle as θ = 10˚24ꞌ.
a) 0.042m
b) 0.402m
c) 0.204m
d) 0.024m

Explanation: The formula for finding the perpendicular can be given as, R*(1-cos (θ/2)). On substitution, we get
10.26*(1- cos (10˚24ꞌ/2)) = 0.042 m.

3. The bisection of chords method involves more accuracy.
a) False
b) True

Explanation: Since the bisection of each chord is involved in this method, this may have an advantage over the remaining methods. The bisection can provide accuracy by involving each step closely.

4. Set a perpendicular offset for A and B using the radius and the angle given. R = 34.76m and θ = 14˚76ꞌ.
a) 2.08m
b) 0.82m
c) 0.28m
d) 8.02m

Explanation: The perpendicular offset can be set by using the formula, R*(1-cos (θ/4)). On substitution, we get
34.76*(1-cos (14˚76ꞌ/4)) = 0.28 m.

5. Which of the following represents the replication of versine?
a) 1-cos θ
b) 1-cosec θ
c) 1-cot θ
d) 1-sin θ

Explanation: Versine is the indication of the inversion of sine i.e., sin-1. Among the following, 1-cos θ represents the versine value. This is done for improving technical knowledge.

6. Perpendicular offsets can be set out after__________
a) Resection
b) Intersection
c) Trisection
d) Bisection

Explanation: Bisection is the main process involved in the successive bisection of the chords method. For the erection of perpendicular offsets it is must for developing the bisection process, as it provides the points necessary for perpendicular offsets.

7. Which of the following describes the advantage of bisection of chords method?
a) Setting out more chords
b) Setting out more parallels
c) Setting out more points
d) Setting out more perpendiculars

Explanation: The successive bisection of chords involve in determining the offsets points and also in erecting the perpendicular offsets. The main advantage of this method involves generation of more amount of points by which this process can be continued.

8. Find the perpendicular offset using successive bisection of chords, with radius 34.98m and length 12.65 m.
a) 0.75m
b) 0.57m
c) 5.07m
d) 7.05m

Explanation: The formula in successive bisection of chords for erecting a perpendicular can be given as $$R – (R^2 – (\frac{l}{2})^2)^{1/2}$$. On substitution, we get
$$34.98 – (34.98^2- (\frac{12.65}{2})^2)^{1/2} = 0.57m.$$

9. The successive bisection of chords comes under which of the following category?
a) Transition curve
b) Reverse curve
c) Compound curve
d) Simple curve

Explanation: The simple curve setting methods involve certain category off which, the successive bisection of chords is one of them. It is a tedious procedure because it involves the bisection of each chord.

10. Perpendicular chords can be obtained by using the successive bisection method.
a) True
b) False

Explanation: The successive bisection method involves certain procedures among which the erection of perpendicular offsets is also present. This can be achieved by using the formula obtained by solving the procedure.

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