The length of a uniform ladder of massm is 1. It leans against a smooth wall making an angle theta with the horizontal. What should be the force of friction between the floor and ladder so that the ladder does not slip ?

The length of a uniform ladder of massm is 1. It leans against a smoot

1.	The length of a uniform ladder of massm is 1. It leans against a smooth wall making an angle theta with the horizontal. What should be the force of friction between the floor and ladder so that the ladder does not slip ?
Answer» Solution :Let the reaction at P and Q be `N_(1)` and `N_(2)` respectively as shownin fig. For the equilibrium of the ladder, `N_(2)=mg `and `N_(1)=F` where F is the force of friction between the ladder and the floor. Taking MOMENTS about Q. `N_(1)xxPQ sin theta=mg XX(PQ)/(2) costheta` `N_(1)=(1)/(2)mgcot theta` Force of friction `F=N_(1)=(1)/(2)mg cot theta`