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 d2 (< d1). The volume V1 immersed in liquid of density d1 is

Vdg=V1d1g+V2d2g…..(1) also, V=V1+V2Vd2g=V1d2g+V2d2g…….(2)eq(1)−eq(2)Vg⁡d−d2=V1gd1−d2V1=Vd−d2d1−d2

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 d2 (< d1). The volume V1 immersed in liquid of density d1 is

Vdg=V1d1g+V2d2g…..(1) also, V=V1+V2Vd2g=V1d2g+V2d2g…….(2)eq(1)−eq(2)Vg⁡d−d2=V1gd1−d2V1=Vd−d2d1−d2

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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 d₂ (< d₁). The volume V₁ immersed in liquid of density d₁ is

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

$\frac{d_{1}}{d_{2}} V$

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

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

answer is A.

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Detailed Solution

$\begin{array}{l} Vdg = V_{1} d_{1} g + V_{2} d_{2} g \dots . . (1) also, V = V_{1} + V_{2} \\ {Vd}_{2} g = V_{1} d_{2} g + V_{2} d_{2} g \dots \dots . (2) \\ eq (1) - eq (2) Vg (d - d_{2}) = V_{1} g (d_{1} - d_{2}) \\ V_{1} = V (\frac{d - d_{2}}{d_{1} - d_{2}}) \end{array}$