# 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.

28 Points
12 years ago

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

Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We

All the best Karthik Kannan !!!

Regards,

SOUMYAJIT IIT-KHARAGPUR

Rishi Sharma
2 years ago
Dear Student,

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

Thanks and Regards