`A` rod `AB` rests with the end `A` on rough horizontal ground and the end `B` against a smooth vertical wall. The rod is uniform and of weight w. If the rod is in equilibrium in the position shown in figure.Find
(a)frictional force shown at `A`
(b) normal reaction at `A`
(c) normal reaction at `B`.

Explanation

Let length of the rod is 2l. Using the three conditions of equilibrium. Anti- clockwise moment is taken as positive.

(i) `sumF_(x)=0`
`therefore N_(B)-f_(A)=0`
or `N_(B)=f_(A)`……….(i)
(ii)` sumF_(y)=0 `
`therefore N_(A)-w=0`
or `N_(A)=w`........(ii)
(iii) `sum tau_(0)=0`
`thereforeN_(A)(2l cos 30^(@))-N_(B)(2l sin 30^(@))-w(l cos 30^(@))=0`
or `sqrt(3)N_(A)-N_(B)-(sqrt(3))/(2)w=0`........(iii)
Solving these three equations, we get
(a)`f_(A)= (sqrt(3))/(2)w` (b) `N_A)=w`
(c ) `N_(B)=(sqrt(3))/(2)w`