Question

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.Find the density of the material of the sphere in g/cc.
(A) 3.3
(B) 6.4
(C) 7.2
(D) 12.8

Answer 1

Hint
According to the question there is oil contained in the vessel whose density is 0.8g/cc,the oil contains over mercury whose density is 13.6g/cc. A homogeneous sphere floats with half its volume immersed in volume and the other half is in oil.
Now, we will find the density of the material in gm/cc.

Complete step by step answer
First of all the weight of the material is in downward direction.
So, let the weight of the material be W.
$\Rightarrow W = {\rho _{Hg}} \times \dfrac{V}{2} \times g + {\rho _{oil}} \times \dfrac{V}{2} \times g$..................[where V is equal to volume of the material]......equation 1
In the equation $\dfrac{V}{2}$ represents the half volume of the material which is immersed in oil as well as mercury.
Now, we can say W of the material is equal to mg, where m is represent the mass of the material
m=density * volume of the material
$ \Rightarrow \rho \times V \times g = \dfrac{{0.8 \times V \times g}}{2} + \dfrac{{13.6 \times V \times g}}{2}$
Canceling $V \times g$from both sides we get,
$\Rightarrow \rho = \dfrac{{0.8}}{2} + \dfrac{{13.6}}{2} $
$\Rightarrow \rho = \dfrac{{14.4}}{2}$
$\Rightarrow \rho = 7.2gm/cc $

Note
The main formula of this type of question is $W = \rho Vg$, rho is the density of the material which we found in the solution. And the other density like oil and mercury will be given in the question.