A body of mass M is kept on a rough horizontal surface (friction coefficient `= mu`). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on the body is F where :

Explanation

Let f is the force of friction and N is the normal reaction, then the net force by the surface on the body is `F=sqrt(N^(2)+f^(2))`
Let the applied force is F' (varying), applied horizontally then `flemu_(s)N` (adjustable with f = F ). Now if F' is zero, `f=0and F_(min)=N=Mg`
and when F' is increased to miximum value permissible for no motion. `f=mu_(s)N,`
giving `F_(max)=sqrt(N^(2)+mu_(s)^(2)N^(2))=Mgsqrt(1+mu_(s)^(2))`
thefefore we can write `Mg leFleMgsqrt(1+mu_(s)^(2))`