A wedge with a rough circular track `AB`, is fixed on the plane `x x'`. The radius of the track is `R` and the coefficient of friction of the track varies as `mu=mu_(0)x`. Find the work done on mass `m` in moving from `A` to `B`. Here `C` is the centre of the circular track `AB` and `x` is the distance along `+ve x "axis"` from origin `O`.

Explanation

`F=mumgcostheta+mgsintheta`
`mu=mu_(0)x=mu_(0)Rsintheta`
Work done in moving block a small distance `ds` along track
`intdW=intFds`
`W=int_(0)^(x//2)FRd theta=mu_(0)mgRint_(0)^(x//2)sinthetacosthetad theta+int_(0)^(x//2)mgRsinthetad theta`
`W=mgR[(mu_(0))/(2)+1]`