Question

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 horizontal surface on the surface of the body is F, where

• A. $Mg\le f\le Mg\sqrt{1+{\mu }^2}$
• B. $F=\mu MgF$
• C. $F=Mg$
• D. $Mg\ge f\ge Mg\sqrt{1+{\mu }^2}$

Answer 1

Answer: (A)

If R is normal reaction,

Maximum force by surface when friction work

$F=\sqrt{f^2+R^2}=\sqrt{\mu R^2+R^2}$ $(\because f=\mu R)$

$=R\sqrt{{\mu }^2+1}$

Maximum force = R, when there is no friction.

Hence, ranging from R to $R\sqrt{{\mu }^2+1}$

we get $Mg\le f\le mg\sqrt{{\mu }^2+1}$