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 surface on $A$ is $F$ where:

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

Answer 1

Answer: (C)

$Mg\le F\le Mg\sqrt{1+{\mu }^2}$

$\text{If}R\text{is normal reaction,}$

$\text{Maximum force by suaface when friction work}$

$F=\sqrt{f^2+R^2}$

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

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

$\text{Maximun force}=R,\text{when there is no friction.}$

$\text{Hence,}$

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

$\text{we get}\text{M}g⩽F⩽mg\sqrt{{\mu }^2+1}$

option (C) is correct.