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A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10N. The coefficient of static friction between the block and the plane is : $[Take g = 10 m / s^{2}]$

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$\frac{\sqrt{3}}{2}$

$\frac{\sqrt{3}}{4}$

$\frac{1}{2}$

$\frac{2}{3}$

answer is A.

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Detailed Solution

$2 N + mg \sin 30^{o} = μmgcos 30^{o} and 10 = mgsin 30^{o} + μmgcos 30^{o}$

$6 = μmgcos 30^{o} \to (1)$

$4 = mg \sin 30^{o} \to (2)$

$Divide 1 by 2 \frac{3}{2} = μ \sqrt{3} ∴ Coefficient of Friction μ = \frac{\sqrt{3}}{2}$

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