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A particle of mass \( 0.045 \) g reaches terminal velocity where drag equals weight. If the drag force is \( F_D = 1.2\times10^{-6} v^2 \) N with \( v \) in m/s, the terminal velocity is

  • A.6.1 m/s
  • B.36.8 m/s
  • C.9.6 m/s
  • D.19.2 m/s

Answer: D

The weight is \( 4.5\times10^{-5} \times 9.81 = 4.41\times10^{-4} \) N, so \( v^2 = 4.41\times10^{-4}/1.2\times10^{-6} = 368 \) and \( v = 19.2 \) m/s. Cereal grains sit near this figure while chaff settles far lower, which is exactly what an aspirator exploits.

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