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Question

# A car is moving with a speed of 60 m/s on a curved road banked at an angle of 45∘. If the coefficient of static friction between the wheels of the vehicle and the road is 0.4, what should be the minimum radius of turn for the car so that it does not skid? Take g=10 m/s2.

A
175.5 m
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B
154.3 m
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C
170 m
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D
200 m
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Solution

## The correct option is B 154.3 mAt minimum radius , fmax will be acting down the incline, to prevent upward skidding of vehicle. Fcentripetal=mv2r So if radius will be minimum then maximum Fcentripetal will be required, hence limiting value of friction will act i.e fmax Nsinθ+fmaxcosθ=mv2r....(i) where fmax=μsN....(ii) and Ncosθ−fmaxsinθ=mg...(iii) From Eq. (i), (ii), (iii) :- sinθ+μsNcosθcosθ−μsNsinθ=v2rg ⇒v2=(μs+tanθ1−μstanθ)rg ∴v=√rg(tanθ+μs)1−μstanθ m/s Putting θ=45∘ and μs=0.4: 602=(0.4+tan45∘1−0.4×tan45∘)×r×10 ⇒3600=1.40.6×r×10 ∴r=3600×0.61.4×10=154.3 m Here, radius is the minimum radius for safe travelling on the banked road.

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