Properties Of Solids And Liquids Question 193
Question: A vessel contains oil (density = 0.8 gm/cm3) over mercury (density = 13.6 gm/cm3). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in gm/cm3 is[IIT-JEE 1988]
Options:
A) 3.3
B) 6.4
C) 7.2
D) 12.8
Show Answer
Answer:
Correct Answer: C
Solution:
As the sphere floats in the liquid.
Therefore its weight will be equal to the upthrust force on it Weight of sphere $ =\frac{4}{3}\pi R^{3}\rho g $ .(i)
Upthrust due to oil and mercury $ =\frac{2}{3}\pi R^{3}\times {\sigma _{oil}}g+\frac{2}{3}\pi R^{3}{\sigma _{Hg}}g $ .(ii)
Equating (i) and (ii) $ \frac{4}{3}\pi R^{3}\rho g=\frac{2}{3}\pi R^{3}0.8g+\frac{2}{3}\pi R^{3}\times 13.6g $
$ \Rightarrow 2\rho =0.8+13.6=14.4\Rightarrow \rho =7.2 $
