Circular MotionEasy

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:

Options

A.

gR2μs+tan θ1-μs tan θ

B.

gRμs+tan θ1-μstan θ

C.

gRμs+tan θ1-μs tan θ

D.

gR2μs+tan θ1-μs tan θ

Solution


N = mg cos θ+mv2rsin θ
fmax = μmg cos θ + μmv2rsin θ
mg sin θ + μmg cos θ + μmv2rsin θ=mv2r cos θ
g sin θ + g cos θ = V2r(cos θ - μ sin θ)
grtan θ+μ1+μ tan θ=V2

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