A small steel ball of mass `m` and radius `r` is falling under gravity through a viscous liquid of coefficient of viscosity `eta`. If `g` is the value of acceleration due to gravity. Then the terminal velocity of the ball is proportional to (ignore buoyancy)

Options

A. `V prop (mgr)/(eta)`
B. `V prop mg eta r`
C. `V prop (mg)/(eta r)`
D. `V prop (eta mg)/(r )`

Answer

C

Explanation

`F=6pi eta ` rv i.e., v has the dimensions of `(F)/(eta r) " or" (mg)/(eta r)`