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A block of mass m. lying on a horizontal pane, is acted upon by it horizontal force P and another force Q, inclined at an angle $θ$ to the vertical. The block will remain in equilibrium if the coefficient of friction between it and the surface is (assume P > Q)

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$(P \sin θ - Q) / (m g - Q \cos θ)$

$(P - Q \sin θ) / (m g + Q \cos θ)$

$(P \cos θ + Q) / (m g - Q \cos θ)$

$(P + Q \sin θ) / (m g + Q \cos θ)$

answer is B.

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Detailed Solution

Frictional force $= μ R = μ (m g + Q \cos θ)$ and horizontal push $= P - Q \sin θ$ For equilibrium, we have

$μ (m g + Q \cos θ) = P - Q \sin θ \Rightarrow μ = \frac{P - Q \sin θ}{m g + Q \cos θ}$

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