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Question

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

  1. fraction numerator left parenthesis P plus Q sin invisible function application theta right parenthesis over denominator left parenthesis m g plus Q cos invisible function application theta right parenthesis end fraction    
  2. fraction numerator left parenthesis P cos invisible function application theta plus Q right parenthesis over denominator left parenthesis m g minus Q sin invisible function application theta right parenthesis end fraction    
  3. fraction numerator left parenthesis P plus Q cos invisible function application theta right parenthesis over denominator left parenthesis m g plus Q sin invisible function application theta right parenthesis end fraction    
  4. fraction numerator left parenthesis P sin invisible function application theta minus Q right parenthesis over denominator left parenthesis m g minus Q cos invisible function application theta right parenthesis end fraction    

The correct answer is: fraction numerator left parenthesis P plus Q sin invisible function application theta right parenthesis over denominator left parenthesis m g plus Q cos invisible function application theta right parenthesis end fraction


    By drawing the free body diagram of the block for critical condition

    F equals mu R ÞP plus Q sin invisible function application theta
    equals mu left parenthesis m g plus Q cos invisible function application theta right parenthesis
    therefore mu equals fraction numerator P plus Q sin invisible function application theta over denominator m g plus Q cos invisible function application theta end fraction

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