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Question

# A vessel contains oil (ρ=0.8 gm/cm3) over mercury (ρ=13.6 gm/cm3). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. Then density of material of the sphere in gm/cm3 is

A
3.3
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B
6.4
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C
7.2
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D
2.8
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Solution

## The correct option is C 7.2Half of sphere immersed in mercury and half in oil. Thus there will be upthrust due to both liquids. Lets ρd be the density of sphere Upthrust due to buoyancy = Mass of mercury displaced + mass of oil displaced Upthrust =v2×13.6×g+v2×0.8×g Downward gravitational force due to sphere = v×ρd×g Downward gravitational force = Upthrust due to buoyancy v×ρd×g=v2×13.6×g+v2×0.8×g ρd=7.2 gm/cm3

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