Physics-
General
Easy

Question

A thin movable plate is separated from two fixed plates P subscript 1 and P subscript 2 by two highly viscous liquids of coefficients of viscosity n subscript 1 and n subscript 2 as shown, where n subscript 2 end subscript equals 9 n subscript 1 end subscript. Area of contact of movable plate with each fluid is same. If the distance between two fixed plates is ‘h’, then the distance ‘h subscript 1 end subscript’ of movable plate from upper plate such that movable plate can be moved with a finite velocity by applying the minimum possible force on movable plate is ( assume only linear velocity distribution in each liquid).

  1. fraction numerator h over denominator 4 end fraction    
  2. fraction numerator h over denominator 2 end fraction    
  3. fraction numerator h over denominator 6 end fraction    
  4. fraction numerator h over denominator 3 end fraction    

The correct answer is: fraction numerator h over denominator 4 end fraction


    Viscous force due to upper liquid equals n subscript 1 end subscript A open parentheses fraction numerator v minus o over denominator h subscript 1 end subscript end fraction close parentheses
    Viscous force due to lower liquid = n subscript 2 end subscript A open parentheses fraction numerator v minus o over denominator h minus h subscript 1 end subscript end fraction close parentheses
    If total force is minimum
    fraction numerator d over denominator d h subscript 1 end subscript end fraction open square brackets fraction numerator n subscript 1 end subscript over denominator h subscript 1 end subscript end fraction plus fraction numerator n subscript 2 end subscript over denominator h minus h subscript 1 end subscript end fraction close square brackets equals 0

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S o comma space f space i s space o n e minus space o n e.
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T h u s comma space f u n c t i o n space i s space n o t space o n t o.

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