A body of mass M is kept on a rough horizontal surface (friction coefficient `=μ). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the horizontal surface on the surface of 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_(5)N` (adjustable with f=F).
Now if F' zero, f=0 and `F_("min")=N=Mg` and when F is increased to maximum value permissible for no motion `f=mu_(5)N,` giving `F_("max")=sqrt(N^(2)+mu_(s)^(2)N^(2))=Mgsqrt(1+mu_(s)^(2))`
therefore we can write `MgleFleMgsqrt(1+mu_(s)^(2))`