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Question

If a car is moving at a velocity v in a circular road with coefficient of friction μ and banking angle θ. Find the radius of the road such that friction force doesn't act on the car in the radial direction.

A
r=v2gtanθ
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B
r=vgtanθ
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C
r=v2gtanθ
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D
r=v2g
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Solution

The correct option is A r=v2gtanθ
For the force of friction to be zero, the centripetal force has to be provided by the normal reaction force only. Which means N sin(θ)=mv2r .....................(1)
now the other component of the normal reaction N cos(θ) balances the weight of the car.
N cos(θ)=mg ....................(2)

Using this in (1) we get
mg tan(θ)=mv2r
r=v2g tan(θ)

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