A body is moving down a long inclined plane of angle of inclination `'theta`' for which the coefficient of friction varies with distance x as `mu`(x) = kx , where k is a constant . Here x is the distance moved by the body down the plane . The net force on the body will be zero at a distance `x_(0)` is given by ..........

Explanation

`F=mg sin theta-f`
`N=mg cos theta," "f=muN=mumg cos theta`
`F=mg sin theta-mu mg cos theta`
`F=mg(sin theta-kx cos theta)`
If `F=0," "sin theta-kx_(0)cos theta=0 rArr x_(0)=(tan theta)/(k)`