`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 shown at `A`
(b) normal reaction at `A`
(c) normal reaction at `B`.

Explanation

Let length of the rod be `2l`. Using the three condition of equibrium. Anticlockwise moment is taken as positive.
(i) `sumF_(x) =0` `rArr :.` `N_(B) -f_(A) =0`
or `N_(B) = f_(A)` …(i)
(ii) `sumF_(y) =0` `rArr :.` `N_(B) -w =0`
or `N_(A) = w` …(ii)
(iii)`sum pi_(0) =0`
:. ` N_(A) (2l cos30^(@)) - N_(B) (2l sin30^(@)) - w(l cos30^(@)) = 0`
or ` sqrt3N_(A) - N_(B) -sqrt(3)/(2)w=0` ...(iii)
Solving these three eqution, we get
`f_(A) = sqrt(3)/(2)w` (b) `N_(A) = w` (c) `N_(B) = sqrt(3)/(2)w`