First slide

Pressure in a fluid-mechanical properties of fluids

Question

A vessel contains oil (density = 0.8 g/cm³) over mercury (density = 13 .6 g/cm³). A uniform sphere floats with half its volume immersed in mercury and the other half in oil.
The density of the material of sphere in g/cm³ is

Moderate

A

3.3
B

6.4
C

12.8
D

7.2

Solution

$\begin{matrix} Weight = buoyant force \\ \Rightarrow V ρ g = \frac{V}{2} ρ_{Hg} g + \frac{V}{2} ρ_{oil} g \\ \Rightarrow ρ = \frac{ρ_{Hg} + ρ_{oil}}{2} = \frac{13.6 + 0.8}{2} = \frac{14.4}{2} = 7.2 \end{matrix}$

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