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 race car to aviod wear and tear on its tyres .
maximum permissible speed to aviod slipping ?

Explanation

Here, ` r = 400 m , theta = 10^(@) , mu = 0.2 `
(i) optimum speed of the car to aviod wear and
tear ` upsilon = sqrt(rd tan ) = sqrt(400 xx 9.8 tan 10^(@) )= `
` = sqrt(400 xx 9.8 xx 0 .1763) = sqrt(69. 1.1)`
` = 26 . 29 m//s `
(ii) maximum permissible speed is ` upsilon_(max) = sqrt((r g(mu + tan theta))/(1- mu tan theta) `
` = sqrt((400 xx 9.8 (0.2 + 0.1763))/(1 - 0 .2 xx 0. 1763 `
` = 39 . 10 m // s ` .