NEET 2016 Phase 1 · PhysicsBankingPrevious Year Question
A car is negotiating a curved road of radius R. The road is banked at an angle θ and the coefficient of friction between the tyres and the road is μs. The maximum safe velocity on this road is:
Answer: (B) √(gR·(μs + tanθ)/(1 − μs tanθ)). Correct Answer (B) Solution: At max speed friction acts down the incline.
- A.√(gR²·(μs + tanθ)/(1 − μs tanθ))
- B.√(gR·(μs + tanθ)/(1 − μs tanθ))✓
- C.√((g/R)·(μs + tanθ)/(1 − μs tanθ))
- D.√((g/R²)·(μs + tanθ)/(1 − μs tanθ))
Correct Answer
(B) √(gR·(μs + tanθ)/(1 − μs tanθ))
Solution & Explanation
Correct Answer (B) Solution: At max speed friction acts down the incline. Vertical: N cosθ = mg + μsN sinθ. Horizontal (centripetal): N sinθ + μsN cosθ = mv²/R. Dividing: v²/(gR) = (tanθ + μs)/(1 − μs tanθ) ⇒ v = √(gR·(μs + tanθ)/(1 − μs tanθ)).
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