Question

A vessel containing oil having density 0.8 g/cc over mercury whose density is 13.6 g/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?
A- 3.3
B- 6.4
C- 7.2
D- 12.8

Answer 1

Hint: we are given the situation having two liquids in a container, oil and mercury. The density of mercury is greater than the density of oil. We know that the one with higher density, goes down. So, mercury is below and oil is above it. The sphere when dipped into the container, it floats half in mercury and half in oil. Thus, the density of the sphere is greater than the oil but lesser than the mercury.

Complete step by step answer:
Density of oil=\[\xi \]=0.8 g/cc
Density of mercury=\[\zeta \]=13.6 g/cc
We know density is given by, \[d=\dfrac{m}{V}\], where m is the mass and V is the volume. So, mass can be written as \[m=dV\]
Let us assume that the volume of the sphere is 2V and mass be m.
Since, half of the sphere is inside oil and other half inside mercury, thus,
$ 2dV=0.8\times V+13.6\times V \\ $
$ \Rightarrow 2d=0.8+13.6 \\ $
$ \Rightarrow d=\dfrac{14.4}{2} \\ $
$ \therefore d=7.2g/cc \\ $
So, the density of the sphere comes out to be 7.2 g/cc

So, the correct answer is “Option C”.

Note:
Density plays a very important role in determining whether a solid placed in a liquid will float or sink. If the density of the solid is less than the density of the liquid, then it floats. If the density of the solid is equal to the density of the liquid then it floats but completely submerged. If the density of the solid is greater than the density of the liquid then it sinks.