A car is negotisting a curved road of radius `R` . The road is banked at an angle theta. The coefficient of friction between the tyres of the car and the road is `mu_(s)` . The maximum safe velocity on this road is:

Options

A. `sqrt(gR^(2) (mu_(s) + tan theta)/(1 - mu_(s) tan theta))`
B. `sqrt(gR (mu_(s) + tan theta)/(1 - mu_(s) tan theta))`
C. `sqrt((g)/(R) (mu_(s) + tan theta)/(1 - mu_(s) tan theta))`
D. `sqrt((g)/(R^(2)) (mu_(s) + tan theta)/(1 - mu_(s) tan theta))`

Explanation

`N cos theta = F sin theta + mg`
`N sin theta + F cos theta = (mv^(2))/(R )`
`F = mu_(s) N`
`(v^(2))/(Rg) = (N sin theta + mu_(s) N cos theta)/(N cos theta - mu_(s) N sin theta)`
`v = v_(max) = sqrt(gR ((tan theta + mu_(s))/(1 - mu_(s) tan theta)))`