The terminal velocity of a small sphere falling through a viscous liquid is proportional to
Correct answer: B. the square of the radius of the sphere
- 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.
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About Terminal Velocity
Terminal velocity is the constant speed reached when gravitational force is balanced by fluid resistance. The topic covers drag, buoyant force, the conditions for zero acceleration, and how viscosity, object size, shape and density affect the limiting speed, with a distinction between free fall before and after terminal velocity.
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