Question 162 of 210

A body of mass $1kg$ rests on a horizontal floor with which it has a coefficient of static friction $\dfrac{1}{\sqrt{3}}$. It is desired to make the body move by applying the minimum possible force $FN$. The value of $F$ will be _______.(Round off to the Nearest Integer) [Take $g=10{ms}^{-2}$ ]

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Answer: 5

$F\cos \theta =\mu N$
$\Rightarrow F\sin \theta +N=mg$
$\Rightarrow F=\dfrac{\mu mg}{\cos \theta +\mu \sin \theta }$
${F}_{\min }=\dfrac{\mu mg}{\sqrt{1+{\mu }^{2}}}=\dfrac{\dfrac{1}{\sqrt{3}}\times 10}{\dfrac{2}{\sqrt{3}}}=5$