Physics Fluid Dynamics PMDC Conceptual Practice
PMDC Verified Question 3 of 37
A metal sphere of radius \( r \) is dropped into a tank of water. As it sinks at a steady speed \( v \), it experiences a drag force \( F \) given by the empirical relation \( F = k r v \), where \( k \) is a constant. What are the SI base units of \( k \)?
A
\( \text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-1} \)
B
\( \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-1} \)
C
\( \text{kg} \cdot \text{m}^{-2} \cdot \text{s}^{-2} \)
D
\( \text{kg} \cdot \text{m} \cdot \text{s}^{-2} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \( \text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-1} \)
Concept:

Dimensional analysis is used to determine the SI units of an unknown constant by isolating it and substituting the known base units of the other variables.

Formula:

$$ k = \frac{F}{r \cdot v} $$

Solution:

  • The SI base unit for Force (\( F \)) is \( \text{kg} \cdot \text{m} \cdot \text{s}^{-2} \).
  • The SI base unit for radius (\( r \)) is \( \text{m} \).
  • The SI base unit for speed (\( v \)) is \( \text{m} \cdot \text{s}^{-1} \).
  • Substitute the units: \( k = \frac{\text{kg} \cdot \text{m} \cdot \text{s}^{-2}}{\text{m} \cdot (\text{m} \cdot \text{s}^{-1})} \).
  • Simplify the expression: \( k = \text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-1} \).


Why other options are incorrect:

Failing to cancel the meter unit in the numerator and denominator or misidentifying the unit of force leads to the incorrect options.

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.

Previous Question All Fluid Dynamics MCQs Next Question

Want to solve full-length papers under timed exam conditions?

Practice with zero-scroll lockdown sprints, dynamic latency zone timers, live peer selection telemetry, and the automated Amber mistake recovery loop.

Enter Arena Sprint iOS App Android App