Question

A body of mass $M$ is kept on a rough horizontal surface [friction coefficient $=u$). A person is trying to pull the body by applying a horizontal force $F$ but the body is not moving then

• 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)

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

Answer 2

Maximum force applied $F=\sqrt{f^{2}+R^{2}}$, where $f =$ force of friction Since, $f=\mu R$ Then, $f=\sqrt{\mu^{2} R^{2}+R^{2}}=R \sqrt{\mu^{2}+1}$ Now, if $\mu=0, F=R s$ which is minimum force $\because R=m g$ $\therefore M g \leq F \leq M g \sqrt{\mu^{2}+1}$