Physics And Measurement Question 266

Question: A spherical body of mass m and radius r is allowed to fall in a medium of viscosity $ \eta $ . The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity (v) is called time constant $ (\tau ) $ . Dimensionally $ \tau $ can be represented by:

Options:

A) $ \frac{mr^{2}}{6\pi \eta } $

B) $ \sqrt{( \frac{6\pi mr\eta }{g^{2}} )} $

C) $ \frac{m}{6\pi \eta rv} $

D) None of these

Show Answer

Answer:

Correct Answer: D

Solution:

[d] $ F=6\pi \eta rv $
$ \Rightarrow mg=6\pi \eta rv $ (dimensionally) Check options dimensionally



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