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

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

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

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Solution

The correct option is A $(\frac{d - d_{2}}{d_{1} - d_{2}}) V$
As the body is floating the weight of boy must be equal to weight water displaced,
$V d = V_{1} d_{1} + V_{2} d_{2}$ -------------(1)
and $V_{1} + V_{2} = V$ [given]
$\Rightarrow V_{2} = (V - V_{1})$ -------------(2)

Substituting (2) in (1),
$\Rightarrow V d = V_{1} d_{1} + V d_{2} - V_{1} d$
$\Rightarrow V_{1} (d_{1} - d_{2}) = V d - V d_{2}$
$\Rightarrow V_{1} = \frac{V (d - d_{2})}{d_{1} - d_{2}} = (\frac{d - d_{2}}{d_{1} - d_{2}}) V$

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