(a) Find the maximum speed at which a car turn round a curve of 30 m radius on a level road if the coefficient of friction between the tyres and the road is `0.4` [ acc. Due to gravity = `10 m // s^(2)`]
(b) For traffic moving at 60 km/hr , if the radius of the curve is `0.1` km , what is the correct angle of banking of the road ? ( g = `10 m // s^(2))`

Explanation

(a) Here , for turning , centripetal force is provided by friction so ,
`[(mv^(2))/(r)] lt f_(L) , i.e., (mv^(2))/(r) lt mu "mg" ` [ as `f_(L) = mu "mg"]`
i.e., `" " v lt sqrt(mu "gr")` so that `v_("max") = sqrt(mu "gr")`
Here `mu = 0.4` r = 30 m and g = `10 m//s^(2)`
So , `v_("max") = sqrt(0.4 xx 30 xx 10) = 11 m//s`
(b) In case of banking , tan `theta = (v^(2)// "rg")`
Here , `" " v = 60("km")/("hr") = 60 xx (5)/(18) m//s = (50)/(3) m//s`
r = `0.1` km and 100 m and g = `10 m//s^(2)`
So , tan `theta = (50 xx 50)/(3 xx 3 xx 100 xx 10) i.e , theta = tan^(-1)[(5)/(18)]`