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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 θ to the vertical upwards. The block will remain in equilibrium, if minimum coefficient of friction between it and the surface is

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a

(P+Qsinθ)(mg-Qcosθ)

b

(Pcosθ+Q)(mg-Qsinθ)

c

(P-Qcosθ)(mg+Qsinθ)

d

(Psinθ-Q)(mg-Qcosθ)

answer is A.

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Detailed Solution

N = mg - QcosθP+Qsinθ=μN=μ(mg-Qcosθ)∴  μ=(P+Qsinθ)(mg-Qcosθ)
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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 θ to the vertical upwards. The block will remain in equilibrium, if minimum coefficient of friction between it and the surface is