Q. 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
A) $F = Mg$
B) $F = \mu Mgf$
C) $Mg \leq F \leq Mg\sqrt{1 + \mu^{2}}$
D) $Mg \geq F \geq Mg\sqrt{1 + \mu^{2}}$
Explanation
(c) Maximum force by surface when friction works
$F = \sqrt{f^{2} + R^{2}} = \sqrt{(\mu R)^{2} + R^{2}} = R\sqrt{\mu^{2} + 1}$
Minimum force =$\ R$ where there is no friction
Hence ranging from $R$ to $R\sqrt{\mu^{2} + 1}$
We get, $Mg \leq F \leq Mg\sqrt{\mu^{2} + 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.