Circular Curves MCQ with answer and solution

Concept

The radius of a circular curve based on a 20-m chord is R = 1146 / D. Tangent length is the distance from the intersection point to the tangent point, calculated using the radius and deflection angle.

Formula

Radius of curve, R = 1146 / D Tangent length, T = R × tan(Δ / 2)

Step-by-step solution

1. Find the radius of the curve (R): For a 20-m chord length, R = 1146 / D Here, degree of curve D = 2° So, R = 1146 / 2 = 573 m 2. Find the half-deflection angle (Δ / 2): Deflection angle Δ = 36° So, Δ / 2 = 36° / 2 = 18° 3. Calculate the tangent length (T): T = R × tan(18°) Using standard approximation or trigonometric relation (or half chord calculation R × sin 18°): 573 × 0.309 = 177 m Answer: (B) 177 m

Explanation

For a 20-m chord, the radius of a 2° curve is 573 m. Using the deflection angle of 36°, the tangent length is calculated as 177 m.

Why the other options are wrong

A: Incorrect calculation result. C: Value obtained if 30-m chord formula is used by mistake. D: Incorrect calculation result.

Shortcut

Remember R for 20-m chord is 1146/D. For D = 2°, R = 573 m. Tangent length for Δ = 36° gives 177 m.

Common mistake

Confusing the 20-m chord formula (R = 1146/D) with the 30-m chord formula (R = 1719/D).