Si units and graphs

Question

terminal velocity = 0.23(Density of sphere - Density of oil)g(Radius squared) where g is acceleration due to gravity.
since terminal velocity unit is ms^-1, it is not equal to the units on the other side of kgm^-3 x ms^-2 x m^2, which then equals kgs^-2 which is clearly not equal to ms^-1 what is going on here. The question was in a mock paper, and this is the relationship between velocity and radius.

Answer 1

I suspect that the coefficient of 0.23 is really some constant that has a value of 0.23 in SI units, instead of a pure number.  If so, its units must be ms/kg so that when multiplied by kg/s², you get m/s.

 

Then

 

v_f = k(ρ_s - ρ_o)gr²

 

where

 

k = 0.23 ms/kg

 

It probably comes from the slope of a linear plot of measured terminal speed vs. measured (ρ_s - ρ_o)gr².  Does this sound reasonable?