A circular race track of radius 400 m is banked at an angle of 10°. If the coefficient of friction between the wheels of a race car and the road is 0.2 , what is the (i) optimum speed of the car to avoid wear and tear on its tyres (ii) maximum permissible speed to avoid slipping, g = 9.8 m/s2.

1The optimum speed of the racing car is given byv0=Rgtanθ12v0=400×9.8×tan10°12v0=26.29 m s-12 The maximum permissible speed is given asvm=Rgμ+tanθ1-μtanθvm=400×9.80.2+0.1761-0.20.176vm=39.08 m s-1

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