Correct Answer - Option 3 : 264 m
Concept:
\(\text{Length of Curve} = R × δ×\frac{\pi}{180}\)
Where,
R = radius of curve, \(\delta\) = deflection angle
Calculation:
Given,
Length of chain = 20 m,
R = 15 chains = 15 × 20 = 300 m,
deflection angle (\(\delta \)) = 50°30' = 50.50° (∵ 1° = 60', So, 30' = 0.5°)
∵ We know that, \(\text{Length of Curve} = R × δ×\frac{\pi}{180}\)
⇒ \(\text{Length of Curve} = 300 × 50.50×\frac{\pi}{180}\)
∴ Length of curve = 264.28 m
The degree of curve is given as,
- For 20 m chain length, \(D_a = \frac{1146}{R}\)
- For 30 m chain length, \(D_a = \frac{1718}{R}\)
Where,
Da = degree of curve and R = radius of the curve