A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force $2\,N$ down the inclined plane. The maximum external force up the inclined plane that does not move the block is $10\,N.$ The coefficient of static friction between the block and the plane is : $[$Take $g = 10\,m/s^2 ]$
JEE MAIN 2019, Difficult
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$m g \sin \theta+2=\mu m g \cos \theta$
$10-m g \sin =\mu m g \cos \theta$
On adding: $(1) + (2)$
$12=2 \mu m g \frac{\sqrt{3}}{2} ; \mu m g=\frac{12}{\sqrt{3}}$
$O n(1)-(2):$
$8=2 m g \times \frac{1}{2} ; m g=8 ; \mu=\frac{\sqrt{3}}{2}$
$10-m g \sin =\mu m g \cos \theta$
On adding: $(1) + (2)$
$12=2 \mu m g \frac{\sqrt{3}}{2} ; \mu m g=\frac{12}{\sqrt{3}}$
$O n(1)-(2):$
$8=2 m g \times \frac{1}{2} ; m g=8 ; \mu=\frac{\sqrt{3}}{2}$
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