First slide

Variation of friction with applied force

Question

A body of mass M is kept on a rough horizontal surface (friction coefficient $μ$ ). 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

Easy

A

$F = M g$
B

$F = μ M g f$
C

$M g \leq F \leq M g \sqrt{1 + μ^{2}}$
D

$M g \geq F \geq M g \sqrt{1 + μ^{2}}$

Solution

Maximum force by surface when friction works
$F = \sqrt{f^{2} + R^{2}} = \sqrt{{(μ R)}^{2} + R^{2}} = R \sqrt{μ^{2} + 1}$
Minimum force when there is no friction
Hence ranging from R to $R \sqrt{μ^{2} + 1}$
We get, $M g \leq F \leq M g \sqrt{μ^{2} + 1}$

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