Fluid Mechanics Viscosity Question 138
Question: A marble of mass $ x $ and diameter 2r is gently released in a tall cylinder containing honey. If the marble displaces mass y (< $ x $ ) of the liquid, then the terminal velocity is proportional to
Options:
A) $ x+y $
B) $ x-y $
C) $ \frac{x+y}{r} $
D) $ \frac{x-y}{r} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ v_{0}=\frac{2}{9}\frac{r^{2}(\rho -\rho ‘)g}{\eta } $ $ Now,x=\frac{4}{3}\pi r^{3}\rho ,,or\rho \propto \frac{x}{r^{3}} $ $ Similarly,\rho ‘\propto \frac{y}{r^{3}} $ $ \therefore v_{0}\propto \frac{x-y}{r} $
BETA
