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A solid metal sphere of radius r is dropped and falls freely through air. The air resistance is taken to be proportional to the cross-sectional area and to the square of the speed. The terminal velocity attained by the sphere then varies with r as which of the following?
- r²
- r
- r^(3/2)
- r^(1/2)
Correct answer: r^(1/2)
Solution
Setting gravitational force equal to the quadratic drag and using the area and mass scalings gives the dependence of terminal speed on radius.
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