First slide

Pressure in a fluid-mechanical properties of fluids

Question

The fraction of a floating object of volume V₀ and density d₀ above the surface of a liquid of density d will be

Moderate

A

$\frac{d_{0}}{d}$
B

$\frac{{dd}_{0}}{d + d_{0}}$
C

$\frac{d - d_{0}}{d}$
D

$\frac{{dd}_{0}}{d - d_{0}}$

Solution

$For the floatation V_{0} d_{0} g = V_{in} dg \Rightarrow V_{in} = V_{0} \frac{d_{0}}{d}$
$\begin{array}{l} ∴ V_{out} = V_{0} - V_{in} = V_{0} - V_{0} \frac{d_{0}}{d} = V_{0} [\frac{d - d_{0}}{d}] \\ \Rightarrow \frac{V_{out}}{V_{0}} = \frac{d - d_{0}}{d} \end{array}$

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