A block of mass m, lying on a horizontal plane, is acted upon by a horizontal force P and another force Q, inclined at an angle θ to the vertical. The block will remain in equilibrium if the minimum coefficient of friction between it and the surface is (assume P > Q)
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a
(P sin θ−Q)/(mg−cos θ)
b
(P−Q sin θ)/(mg+Q cos θ)
c
(P cos θ+Q)/(mg−Q cos θ)
d
(P+Q sin θ)/(mg+Q cos θ)
answer is B.
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Detailed Solution
Frictional force =μR=μ(mg+Q cos θ) and horizontal push =P−Q sin θ For equilibrium, we have μ(mg+Q cos θ)=P−Q sin θ⇒μ=P−Q sin θmg+Q cos θ