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Floatation

A body of den...

Question

A body of density 𝑑 and volume $V$ floats with volume $V_{1}$ of its total volume $V$ immersed in a liquid of density $d_{1}$ and the rest of the volume $V_{2}$ immersed in another liquid of density $d_{2} (< d_{1})$ .The volume $V_{1}$ immersed in liquid of density $d_{1}$ is

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

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

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

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

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Solution

The correct option is C $(\frac{d - d_{2}}{d_{1} - d_{2}}) V$
As given, density of the body $d$ and volume $V$ .

$V d g = V_{1} d_{1} g + V_{2} d_{2} g \dots (i)$

Also, total volume of the body,

$V = V_{1} + V_{2}$

Multiple both sides with $d_{2} g$

$V d_{2} g = V_{1} d_{2} g + V_{2} d_{2} g \dots (i i)$

equation $(i) - (i i)$ , gives

$V g (d - d_{2}) = V_{1} g (d_{1} - d_{2})$

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

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Floatation

Standard IX Physics

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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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