Physics And Measurement Question 85
Question: A small steel ball of radius $ r $ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $ \eta $ . After some time the velocity of the ball attains a constant value known as terminal velocity $ v _{T} $ . The terminal velocity depends on (i) the mass of the ball $ m $ , (ii) $ \eta $ , (iii) $ r $ and (iv) acceleration due to gravity $ g $ . Which of the following relations is dimensionally correct
[CBSE PMT 1992; NCERT 1983; MP PMT 2001]
Options:
A) $ v _{T}\propto \frac{mg}{\eta r} $
B) $ v _{T}\propto \frac{\eta r}{mg} $
C) $ v _{T}\propto \eta rmg $
D) $ v _{T}\propto \frac{mgr}{\eta } $
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Answer:
Correct Answer: A
Solution:
By substituting dimension of each quantity in R.H.S. of option
we get $ [ \frac{mg}{\eta r} ]\ =\ [ \frac{M\times L{{T}^{-2}}}{M{{L}^{-1}}{{T}^{-1}}\times L} ] $ = $ [L{{T}^{-1}}] $ .
This option gives the dimension of velocity.
