A simple circular curve of radius 600 m is to be set out on field. Calculate the value of versed sine for the curve if the deflection angle (Δ) = 120°. 

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SSC JE (Civil) 2023 Official Paper-II (Held On: 04 Dec, 2023 Shift 1)
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  1. 453.33 m
  2. 120 m
  3. 333.33 m
  4. 300 m

Answer (Detailed Solution Below)

Option 4 : 300 m
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Detailed Solution

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Concept:

Versine of curve: The versine is the perpendicular distance of the midpoint of a chord from the arc of a circle.

F2 Savita ENG 22-12-23 D1

where, M = Versine of curve, Δ  = Deflection angle and R = Radius of curve

\(M = R \times (1 - Cos{\Delta\over 2})\)

Calculation:

Given: R = 600 m,  Δ  = 1200

\(M = 600 \times (1 - cos{120\over 2})=300m\)

 

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