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Q.

A block of mass m, lying on a rough horizontal plane, is acted upon by a horizontal force P and another force Q inclined at an angle q to the vertical. The block willremain in equilibrium, if the coefficient of friction between it and the surface is

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a

(P+Qsin⁡θ)/(mg+Qcos⁡θ)

b

(Pcos⁡θ+Q)/(mg−Qsin⁡θ)

c

(P+Qcos⁡θ)/(mg+Qsin⁡θ)

d

(Psin⁡θ−Q)/(mg−Qcos⁡θ)

answer is A.

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Detailed Solution

Here, Friction =μR=μ(mg+Qcos⁡θ) and, Horizontal push =P+Qsin⁡θFor equilibrium μ(mg+Qcos⁡θ)=P+Qsin⁡θ∴ μ=P+Qsin⁡θ(mg+Qcos⁡θ)

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