Properties Of Solids And Liquids Question 252

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} $



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