Fluid Mechanics Viscosity Question 251
Question: A vessel contains oil$ (density=0.8gm/cm^{3}) $ over mercury$ (density=13.6gm/cm^{3}) $ . 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/cm^{3} $ is
Options:
A) 33
B) 6.4
C) 72
D) 12.8
Show Answer
Answer:
Correct Answer: C
Solution:
[c] 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}+13.6g $ $ \Rightarrow ,2\rho =0.8+13.6=14.4\Rightarrow \rho =7.2 $
BETA
