Question

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 _________. (Round off to the Nearest Integer) [Take $g=10 \,ms ^{-2}$ ]

Answer 1

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