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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 $F \mathrm{~N}$. The value of $F$ will be __________ (Round off to the Nearest Integer)
[Take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ ]
Solution:
$\mathrm{F} \cos \theta=\mu \mathrm{N}$
$\mathrm{F} \sin \theta+\mathrm{N}=\mathrm{mg}$
$\Rightarrow \mathrm{F}=\frac{\mu \mathrm{mg}}{\cos \theta+\mu \sin \theta}$
$\mathrm{F}_{\min }=\frac{\mu \mathrm{mg}}{\sqrt{1+\mu^{2}}}=\frac{\frac{1}{\sqrt{3}} \times 10}{\frac{2}{\sqrt{3}}}=5$
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