I came up with a question stated below
"A vessel contains oil (density 0.8g/cc) over mercury (density 13.6g/cc). 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/cc is ?"
The answer to this problem is 7.2 g/cc but this seems incorrect to me. I got 6.4 g/cc
If we consider the oil section only then, the massive force at the surface of lower part of the hemisphere is cancelling it out (Think in 3d), and small force which act on upper surface has vertical component (downwards) as horizontal component are cancelled out, there is a net downward force on sphere by oil (Buoyant force).
Sphere is homogenous, oil and mercury has constant density so dont assume out of the box
As Suggested by BIO's answer let put a small negligible rod in between two hemisphere under consideration then due to that flat surface there is a greater force on that flat surface which compensate other small force acting on curved surface to lead for an upward net force by oil, but in reality we cant assume that, as that flat surface isnt exposed to oil section (but only curved surface)
Excuse for that drawing
Still cant figure it out help