A block slides down an incline of angle `30^(@)` with an acceleration of `g//4` Find the coefficient of kinetic friction .

Answer

`(1)/3sqrt3` .

Explanation

As the block is sliding down with `a = (g)/(4)`
`:. ma = mg sin theta -F`
`(mg)/(4) = mg sin 30^(@)- F = (mg)/(2) -F`
`F = (mg)/(2)-(mg)/(4) = (mg)/(4)`
Also `R =mg cos theta = mg cos 30^(@) = mg sqrt(3)/(2)`
Now , `mu_(k) = (F)/(R) = (1)/(2 sqrt 3)`.