If the diameter of fat globule in a cream separator is reduced to half and the rotational speed of the centrifuge increased to three times, the terminal settling velocity of fat globule is
Options:
(A) decreased to 0.44 times
(B) increased to 0.44 times
(C) decreased to 2.25 times
(D) increased to 2.25 times
Official Answer Key:
D
Step-by-Step Solution & Explanation
Under Stokes' law in a centrifugal field, terminal settling (rise) velocity of a globule V_t ∝ d²×ω² (d = globule diameter, ω = angular/rotational speed of the centrifuge; the radius/other terms held constant).
If d is halved: (d’/d)² = (0.5)² = 0.25.
If ω is tripled: (ω’/ω)² = 3² = 9.
Combined factor = 0.25 × 9 = 2.25 — i.e., the settling velocity is INCREASED to 2.25 times its original value. Answer: (D).
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