a.Find the maximum speed at which a car can 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 `=10m//s^(2)`]
b. For traffic moving at 60km/hr if the radius of the curve is 0.1 km, what is the correct angle of banking of the road? `(g=10m//s^(2))`

Explanation

a. Here for turning, centripetal force is provided by friction so
`[(mv^(2))/r]lt f_(1)` i.e. `(mv^(2))/r lt mu mg` [ as `f_(1)=mu mg`]
i.e.`vlt sqrt(mugr)` so that `v_("max")=sqrt(mu gr)`
Here `mu=0.4,r=30m` and `g=10m//s^(2)`
so `v_("max")=sqrt(0.4xx30xx10=11m//s`
b.In case of banking `tan theta=((v^(2))/(rg))`
Here `v=60 (km)/(hr)=60xx5/18m//s=50/3m//s`
`r=0.1km=100m` and g`=10m//s^(2)`
So `tan theta=(50xx50)/(3xx3xx100xx10)` i.e. `theta=tan^(-1)[5/18]=15.52^(@)`