A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity "" . 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 \(\pi\) , (ii) "" , (iii) r and (iv) acceleration due to gravity g . Which of the following relations is dimensionally correct
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By substituting dimension of each quantity in R.H.S. of option
we get \(\mathrm{mg} : \mathrm{yr} = \left| \begin{matrix} M \times L T^{-2} \\ M L^{-1} T^{-1} \times L \end{matrix} \right|\) = \(\left[ L T^{-1} \right]\) .
This option gives the dimension of velocity.
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