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A body of mass m is kept on a rough horizontal surface (coefficient of friction = $μ$ ) A horizontal force is applied on the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by F, where F is

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$|\vec{F}| = m g$

$|\vec{F}| = μ m g$

$|\vec{F}| \leq m g \sqrt{1 + μ^{2}}$

$|\vec{F}| = m g + μ m g$

answer is C.

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Detailed Solution

$|\vec{F}| = \sqrt{f^{2} + R^{2}} = \sqrt{{(μ R)}^{2} + R^{2}}$
Hence $m g \leq |\vec{F}| \leq m g \sqrt{1 + μ^{2}}$

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