The terminal velocity of a small sphere falling through a viscous liquid is proportional to
- A. the radius of the sphere
- B. the square of the radius of the sphere
- C. the inverse of the radius
- D. the viscosity of the liquid
Explanation
Equating the weight less upthrust to the Stokes drag gives a terminal velocity proportional to r squared and inversely proportional to viscosity, so a sphere of twice the radius falls four times as fast. This is why fine dust hangs in the air for hours while a pebble drops at once. Raising the viscosity lowers the terminal velocity rather than raising it.