Physics
Fluid-Mechanics
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Question

A solid uniform ball of volume V floats on the interface of two immiscible liquids. The specific gravity of the upper liquid is d1  and that of lower one is d2 and the specific gravity of ball is d. The fraction of the volume of the ball in the upper liquid is open parentheses d subscript 1 less than d less than d subscript 2 close parentheses

  1. d subscript 2 over d subscript 1
  2. fraction numerator d subscript 2 minus d over denominator d subscript 2 minus d subscript 1 end fraction
  3. fraction numerator d minus d subscript 1 over denominator d subscript 2 minus d subscript 1 end fraction
  4. d subscript 1 over d subscript 2

The correct answer is: fraction numerator d subscript 2 minus d over denominator d subscript 2 minus d subscript 1 end fraction


    table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell V d g equals x d subscript 1 g plus left parenthesis V minus x right parenthesis d subscript 2 g semicolon V open parentheses d minus d subscript 2 close parentheses equals x open parentheses d subscript 1 minus d subscript 2 close parentheses end cell row cell x over V equals fraction numerator d minus d subscript 2 over denominator d subscript 1 minus d subscript 2 end fraction equals fraction numerator d subscript 2 minus d over denominator d subscript 2 minus d subscript 1 end fraction end cell end table

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