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Question

A block P of mass m is placed on a frictionless horizontal surface. Another block Q of same mass is kept on P and connected to the wall with the help of a spring of spring constant k as shown in the figure. mu subscript s end subscript is the coefficient of friction between P and Q. The blocks move together performing SHM of amplitude A. The maximum value of the friction force between P and Q is

  1. k A    
  2. fraction numerator k A over denominator 2 end fraction    
  3. Zero    
  4. mu subscript s end subscript m g    

The correct answer is: fraction numerator k A over denominator 2 end fraction


    When two blocks performs simple harmonic motion together then at the extreme position ( at amplitude =A)Restoring force F equals K A equals 2 m a Þ a equals fraction numerator K A over denominator 2 m end fraction
    There will be no relative motion between P and Q if pseudo force on block P is less than or just equal to limiting friction between P and Q.
    i.e. m   open parentheses fraction numerator K A over denominator 2 m end fraction close parentheses equalsLimiting friction
    therefore Maximum friction equals fraction numerator K A over denominator 2 end fraction

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