A body of mass 1 kg rests on a horizontal floor
Question:

A body of mass $1 \mathrm{~kg}$ 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 $\mathrm{FN}$. The value of $\mathrm{F}$ will be (Round off to the Nearest Integer)

$\left[\right.$ Take $\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right]$

Solution:

$F \cos \theta=\mu N$

$F \sin \theta+N=m g$

$\Rightarrow F=\frac{\mu m g}{\cos \theta+\mu \sin \theta}$

$F_{\min }=\frac{\mu m g}{\sqrt{1+\mu^{2}}}=\frac{\frac{1}{\sqrt{3}} \times 10}{\frac{2}{\sqrt{3}}}=5$