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_(r )`. 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 ?

Options

A. `v_(T)prop(mg)/(etar)`
B. `v_(T)prop(etar)/(mg)`
C. `v_(T)prop eta rmg`
D. `v_(T)prop(mgr)/(eta)`

Answer

A

Explanation

`mg=F=6pi etar v_(T)," "v_(T)=(mg)/(6 pi eta r), v_(t) prop (mg)/(eta r)`