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 = mu N = mumg cos theta`
`F =mg sin theta - mumg cos theta`
`F =mg (sin theta - kx cos theta)`
if `F = 0, sin theta -kx_(0) cos theta = 0 rArr x_(0) = (tantheta)/(k)`
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