The terminal velocity v of a small steel ball of radius r falling under gravity through a column of viscous liquid of coefficient of viscosity `eta` depends on mass of the bass m, acceleration due to gravity g, coefficient of viscosity `eta` and radius r. Which of the following relations is dimensionally correct ?

Options

A. `v_(T) prop (m g r )/(eta)`
B. `v_(T) prop` m g `eta` r
C. `v_(T) prop (m g)/(r eta)`
D. `v_(T) prop (eta m g)/(r )`

Answer

c

Explanation

`6 pi reta r v = mg, v prop mg//eta r`