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 $g = 10 m / s^{2}$ ]

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2 + m g sin θ = μ m g cos θ m g sin θ − μ m g cos θ = 2 ( 1 ) m g sin θ + μ m g cos θ = 10 ( 2 ) Equation (1) divided by (2): m g ( sin θ + μ cos θ ) m g ( sin θ − μ cos θ ) ​ = 10 − 2 ​ = 5 − 1 ​ ( 1 − μ 3 ​ ) 5 = − ( 1 + μ 3 ​ ) 6 = 4 3 ​ μ μ = 2 3 ​ ​

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