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A body is moving down a long inclined pl...

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 ..........

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F = mg sin `theta -f `
N = mg cos `theta " " , " " f = muN = mu mg "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 implies x_(0) = ("tan" theta)/(k)`
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