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Questions  

A block of mass M rests on a rough horizontal surface as shown. Coefficient of friction between the block and the surface is μ. A force F = Mg acting at angle θ with the vertical side of the block pulls it. In which of the following cases, the block can be pulled along the surface?

a
tanθ≥μ
b
tanθ2≥μ
c
cosθ≥μ
d
cotθ2≥μ

detailed solution

Correct option is D

N=Mg-Fcosθ=Mg-Mgcosθ=2Mgsin2θ2Further, block can be pulled, if F sinθ ≥ μN⇒  2Mgsinθ2·cosθ2≥2μMgsin2θ2⇒  cotθ2≥μ

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