A body of mass $1\, kg$ rests on a horizontal floor with which it has a coefficient of static friction $\frac{1}{\sqrt{3}}$. It is desired to make the body move by applying the minimum possible force $F\, N$. The value of $F$ will be the Nearest Integer) [Take $g =10 \,ms ^{-2}$ ]
JEE MAIN 2021, Difficult
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$F \cos \theta=\mu N$
$F \sin \theta+ N = mg$
$\Rightarrow F =\frac{\mu mg }{\cos \theta+\mu \sin \theta}$
$F _{\min }=\frac{\mu mg }{\sqrt{1+\mu^{2}}}=\frac{\frac{1}{\sqrt{3}} \times 10}{\frac{2}{\sqrt{3}}}=5$
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