Question

A partical of mass `1kg` rests on rought contact with a plane inclined at `30^(@)` to the horizontal and is just about to slip, Find the coefficient of friction between the plane and the particle.

Answer 1

Weight `mg` has two components `mg sin theta` and `mg cos theta`.Block is at rest
:. `N=mg cos theta` …(i)
`f=mg sin theta` …(ii)
Block is about to slip.
:. `f=f_(l)=mu N` …(iii)
Here `mu _(s)= mu`
Solving these three equations, we get
`mu =tan theta=tan 30^(@)`
`=(1)/sqrt(3)`