A raindrop of radius ‘r’ falls in air with terminal speed vt. What is the terminal speed of a raindrop of radius 2r
Question
A raindrop of radius ‘r’ falls in air with terminal speed vt. What is the terminal speed of a raindrop of radius 2r
Solution
The terminal speed of a falling object is determined by the balance between the gravitational force pulling it down and the drag force from the air resistance pushing it up.
For a raindrop falling in the air, the gravitational force is proportional to its volume (which is proportional to r³), and the drag force is proportional to its cross-sectional area (which is proportional to r²).
When the raindrop reaches its terminal speed, these two forces are equal. So, we can write:
F_gravity ∝ r³ and F_drag ∝ r²
At terminal speed, F_gravity = F_drag, so r³ ∝ r². This implies that the terminal speed (vt) is proportional to r.
Therefore, if we double the radius of the raindrop (from r to 2r), the terminal speed will also double. So, the terminal speed of a raindrop of radius 2r is 2vt.
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