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A car is negotiating a curved road of radius R. The road is banked at an angle θ. The coefficient of friction between the tyres of the car and the road is μs. The maximum safe velocity on this road is:

1. √(gR² [μs + tan θ] / [1 − μs tan θ])
2. √(gR [μs + tan θ] / [1 − μs tan θ])
3. √(g / R [μs + tan θ] / [1 − μs tan θ])
4. g / √R² [1 − μs tan θ]

Correct answer: √(gR [μs + tan θ] / [1 − μs tan θ])

Solution

The maximum safe velocity on a banked curve is derived by balancing the forces acting on the car, including friction, normal force, and centripetal force. The correct formula is √(gR [μs + tan θ] / [1 − μs tan θ]).

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