First slide

Fluid statics

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 $V_{1} immersed in liquid of density d_{1} is$

Moderate

A

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

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

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

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

Solution

Vdg = $V_{1} d_{1} g + V_{2} d_{2} g$ ------------(i)
Also V = $V_{1} + V_{2}$
or $V d_{2} g = V_{1} d_{2} g + V_{2} d_{2} g - - - - - - (i i)$
(i) -(ii) gives
$Vg (d - d_{2}) = V_{1} g (d_{1} - d_{2}) or V_{1} = \frac{d - d_{2}}{d_{1} - d_{2}} V$

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