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

Options

A. `3.3`
B. `6.4`
C. `7.2`
D. `12.8`

Answer

C

Explanation

As the sphere floats in the liquid. Therefore its weight will be equal to the upthrust force on it
Weight of sphere `=4/3 pi R ^(3) rho g " "…(i)`
Upthrust due to oil and mercury
`=2/3 pi R ^(3) xx sigma _("oil")g + 2/3 pi R ^(3) sigma _(Hg) g " "...(ii)`
Equation (i) and (ii)
`4/3 pi R ^(3) rho g = 2/3 pi R ^(3) 0.8 g + 2/3 pi R ^(3) + 13.6g`
`implies 2 rho = 0.8 + 13.6 = 14.4 implies rho = 7.2`