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

7.2
D

12.8

Solution

Weight = buoyant force $= \frac{V}{2} ρ_{Hg} g + \frac{V}{2} ρ_{oil} g$
$∴ ρ = \frac{ρ_{Hg} + ρ_{oil}}{2} = \frac{13 .6 + 0 .8}{2} = \frac{14 .4}{2} = 7 .2$

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