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Questions  

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 will

remain in equilibrium, if the coefficient of friction between it and the surface is

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)

detailed solution

Correct option is A

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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