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Friction Basics question from NEET 2019

Q22NEET 2019Medium

Friction Basics

A body of mass $m$ is kept on a rough horizontal surface (coefficient of friction = $\mu$ ). 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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Answer: (d)

Normal reaction $N = mg$ ; static friction $f \le \mu mg$ .
They are perpendicular, so $|\vec{F}| = \sqrt{N^2 + f^2}$ .
$|\vec{F}| \le \sqrt{(mg)^2 + (\mu mg)^2} = mg\sqrt{1+\mu^2}$
So the answer is (d).

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