STANDARD Physics Circular Motion MCQ Question
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
√(g/R) [μₛ + tanθ / 1 - μₛ tanθ]
√(g/R²) [μₛ + tanθ / 1 - μₛ tanθ]
√(gR²) [μₛ + tanθ / 1 - μₛ tanθ]
√(gR) [μₛ + tanθ / 1 - μₛ tanθ]
Correct Answer
Detailed Explanation
For vertical equilibrium on the road, Ncosθ = mg + fsinθ. The centripetal force for safe turning is Nsinθ + fcosθ = mv²/R. Solving these equations gives the maximum velocity vₘₐₓ = √(gR) [μₛ + tanθ / 1 - μₛ tanθ].
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