Question

A vessel contains oil (density `=0.8gm//cm^3`) over mercury (density `=13.6gm cm^3`). 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 `gm//cm^3` is
A. 3.3
B. 6.4
C. 7.2
D. 2

Answer 1

Correct Answer - C
When the sphere of volume V floats,
Weight of the sphere = weight of mercury (of volume `V//2`)+` weight of oil (of volume `V//2`)
or `Vrhog(V//2)xx13.6xxg+(V//2)xx0.8xxg`
or `g=6.8+0.4=7.2g//cm^(3)`