A cyclist rides along the circumference of a circular horizontal plane of radius `R`, with the friction coefficient `mu=mu_(0)(1-(r )/(R ))`, where `mu_(0)` is constant and `r` is distance from centre of plane `O`. Find the radius of the circle along which the cyclist can ride with the maximum velocity, what is this valocity?

Options

A. `sqrt(mu_(0)gR)/(2)`
B. `sqrt(mu_(0)gR)`
C. `sqrt(mu_(0)R)/(R )`
D. `sqrt((mu_(0)gR)/(2))`

Explanation

`(mv^(2))/(r ) =mu_(0)(1-(r )/(R ))mg`
`v^(2)=mu_(0)g(r-(r^(2))/(R ))`
`(dv)/(dr)=0 x_("max")=sqrt(mu_(0)gR)/(2)`