Laws Of Motion Question 53
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 the body is F, where [MP PET 1997]
Options:
A) $ F=Mg $
B)$ F=\mu Mgf $
C) $ Mg\le F\le Mg\sqrt{1+{{\mu }^{2}}} $
D) $ Mg\ge F\ge Mg\sqrt{1+{{\mu }^{2}}} $
Show Answer
Answer:
Correct Answer: C
Solution:
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 $
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} $
