Physics Fluid Dynamics PMDC Conceptual Practice
PMDC Verified Question 20 of 37
A spherical object of radius \( r \) experiences a viscous retarding force \( F \) from a fluid with a coefficient of viscosity \( \eta \) while moving at a slow speed \( v \). According to Stokes' Law, what is the ratio of this retarding force to the object's speed?
A
\( 6 \pi \eta / r \)
B
\( 6 \pi \eta r^2 \)
C
\( 6 \pi \eta / r^2 \)
D
\( 6 \pi \eta r \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \( 6 \pi \eta r \)
Concept:

Stokes' Law calculates the frictional drag force exerted on spherical objects with very small Reynolds numbers (slow speed) in a continuous viscous fluid.

Formula:

$$ F = 6 \pi \eta r v $$

Solution:

  • The question asks for the ratio of the retarding force (\( F \)) to the speed (\( v \)).
  • Isolate \( F/v \) mathematically: \( \frac{F}{v} = \frac{6 \pi \eta r v}{v} \).
  • The \( v \) cancels out, leaving: \( \frac{F}{v} = 6 \pi \eta r \).


Why other options are incorrect:

The radius \( r \) does not appear in the denominator or as a square in Stokes' equation. These options result from confusing algebraic manipulation.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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