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}}} $

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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} $



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