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Physics

Fluid-Mechanics

Easy

Question

A body of density d and volume V floats with volume V₁ of its total volume V immersed in a liquid of density d₁ and the rest of the volume V₂ immersed in another liquid of density $d subscript 2 open parentheses less than d subscript 1 close parentheses$ . The volume immersed in liquid of density d₁ is

$\frac{d_{1}}{d_{2}} V$
$(\frac{d_{1} - d_{2}}{d_{1}}) V$
$(\frac{d + d_{2}}{d_{1} + d_{2}}) V$
$(\frac{d - d_{2}}{d_{1} - d_{2}}) V$

The correct answer is: $open parentheses fraction numerator d minus d subscript 2 over denominator d subscript 1 minus d subscript 2 end fraction close parentheses V$

$V d g equals V subscript 1 d subscript 1 g plus V subscript 2 d subscript 2 g space space space space space space space space space space space space space space space space space space space space space space space.... space space space left parenthesis 1 right parenthesis text Also end text V equals V subscript 1 plus V subscript 2 text or end text V d subscript 2 g equals V subscript 1 d subscript 2 g plus V subscript 2 d subscript 2 g space space space space space space space space space space space space space space space space space space space space space space space space space space.... space left parenthesis 2 right parenthesis V g open parentheses d minus d subscript 2 close parentheses equals V subscript 1 g open parentheses d subscript 1 minus d subscript 2 close parentheses text or end text V subscript 1 equals fraction numerator d minus d subscript 2 over denominator d subscript 1 minus d subscript 2 end fraction V$

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