Maximum value of force F such that block shown in arrangement does not move ....... N

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4-2.Friction

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What is the maximum value of the force $F$ such that the block shown in the arrangement does not move ....... $N$

A

$20$

B

$10$

C

$12$

D

$15$

Solution

$\mathrm{F} \cos \theta=\mathrm{f}$

$\mathrm{F} \cos \theta=\mu(\mathrm{N})$

$\mathrm{F} \cos \theta=\mu(\mathrm{F} \sin \theta+\mathrm{mg})$

$(\mathrm{F} \cos \theta-\mu \mathrm{F} \sin \theta)=\mu \mathrm{mg}$

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

$\mathrm{F}=\frac{\frac{1}{2 \sqrt{3}} \cdot \sqrt{3} \times 10}{\frac{1}{2}-\frac{1}{2 \sqrt{3}} \times \frac{\sqrt{3}}{2}}$

$\mathrm{F} \Rightarrow 5 \times 4=20 \mathrm{N}$

Standard 11

Physics

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