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Question

A vessel contains oil (density 0.8 g/cm2) over mercury (density 13.6 g/cm3). A homogeneous sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of the sphere in  g/cm3 is


A
3.3
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B
6.4
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C
7.2
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D
12.8
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Solution

The correct option is C 7.2
As the sphere floats in the liquid. Therefore, its weight will be equal to the upthrust force on it.

Weight of sphere =43πR3ρg
Upthrust due to oil and mercurry
          =23πR3σoilg+23πR3σHgg
Equating (i) and (ii)
43πR3ρg=23πR3×0.8g+23πR3×13.6g
2ρ=0.8+13.6=14.4ρ=7.2

Physics

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