A stationary uniform rod of mass 'm', length 'l' leans against a smooth vertical wall making an angle `theta` with horizontal floor. Find the normal force & frictional force that is exerted by the floor on the rod ?

Explanation

As the rod is stationary so the linear acceleration and angular acceleration of rod is zero.
i.e., `a_(cm) = 0 , alpha = 0 `
`{:(N_(2)=f),(N_(1)=mg):}}:'a_(am) = 0 `
Torque about any point of the rod should also be zero
`:. alpha = 0 `
`tau_(A) = 0 rArr mg cos theta (l)/(2) + f l sin theta = N_(1) cos theta . l `
` N_(1) cos theta = sin theta f + (mg cos theta)/(2)`
`f = (mg cos theta)/(2 sin theta) = (mg cot theta)/(2)`