A vessel contains oil (density= 0.8 g/cc) over mercury (dens=13.6 g/cc). A homogenous shphere floats with half its volume immersed in mercury and the other half in oil the density of the material n gm/cc is _____

please explain your answer too.

PS.- one of my main doubts is whether oil will exert any buoyant force on the sphere.

Dear Karthik Kannan,

Ans:- The total weight is balanced by the displaced volumess of the two different fluids. Let it,s Vol is V and the density is n. Then the equilibrium condition should be

 Vng=V/2(0.8)g+V/2(13.6)g

or n=0.4+6.8=7.2 gm/cc(ans)

Regarding to your 2nd qsn you can just see that we have taken the sum of the two buoyant forces.So, everyone should have it's own contribution

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Dear Student,
Please find below the solution to your problem.

The mass of sphere be m
m=dv ,
where d is density and v is volume
So we have m = Mo​+mm​
⇒ dv = do​×2v ​+ dm​×2v​
⇒ d = 2do ​+ dm​​
⇒ d = 20.8+13.6
​⇒ d = 7.2

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