Banking Of Roads

Question

A car moves on a circular banked road of radius 100 m with a speed of 20 m/s. What should be the angle of banking if no friction is required? (g = 10 m/s²)

RankGuru · Accepted Answer

1. **Ideal Banking**: For a car to turn without relying on friction, the horizontal component of the normal force must provide the entire centripetal force.
2. **Formula**: $	an 	heta = \frac{v^2}{rg}$.
3. **Substitute Values**:
   - $v = 20$ m/s $\implies v^2 = 400$.
   - $r = 100$ m.
   - $g = 10$ m/s$^2$.
4. **Calculation**:
   - $	an 	heta = \frac{400}{100 	imes 10} = \frac{400}{1000} = 0.4$.
5. **Inverse**: $	heta = 	an^{-1}(0.4)$.

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Banking Of Roads

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