A) \[{{v}_{T}}\propto \frac{mg}{\eta r}\]
B) \[{{v}_{T}}\propto \frac{\eta r}{mg}\]
C) \[{{v}_{T}}\propto \eta rmg\]
D) \[{{v}_{T}}\propto \frac{mgr}{\eta }\]
Correct Answer: A
Solution :
By substituting dimension of each quantity in R.H.S. of option we get \[\left[ \frac{mg}{\eta r} \right]\ =\ \left[ \frac{M\times L{{T}^{-2}}}{M{{L}^{-1}}{{T}^{-1}}\times L} \right]\]=\[[L{{T}^{-1}}]\]. This option gives the dimension of velocity.
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