7. The drag force on a particle moving at a speed v in a medium is of the form F=ζv,
where the drag coefficient ζ depends on the particle’s shape and size and on properties of
the medium. If length is measured in cm, mass in g, and time in s, then ζ has units:
a. g
b. g/(cm s)
c. g/s
d. g cm2/s

The drag coefficient ζ in the linear drag force F = ζv has units of g/(cm s) in the cgs system (grams, centimeters, seconds). This matches option b, as confirmed by dimensional analysis.

Dimensional Analysis

Force F has units of mass × length / time², or g·cm/s². Velocity v has units of cm/s. Thus, ζ = F/v yields (g·cm/s²) / (cm/s) = g/(s·cm), which simplifies to g/(cm s).​

Option a (g) fails because it lacks time and length dimensions, equating to mass alone, not matching force/velocity.
Option c (g/s) misses the length dimension (cm), making it mass/time instead of mass/(length·time).
Option d (g cm²/s) includes excess length (cm²), which would imply force proportional to v times area, not linear drag.​

The drag coefficient units in the cgs system are crucial for understanding particle motion through viscous media, especially in linear drag regimes like F=ζv. This key phrase “drag coefficient units cgs” highlights dimensional analysis where ζ ensures force balances with velocity.

Linear Drag Physics

Linear drag applies to low Reynolds number flows, such as small particles in fluids, following Stokes’ law where drag force F equals ζ times speed v. ζ incorporates medium viscosity η, particle size (e.g., radius r), and shape factors, yielding units g/(cm s) or dyne·s/cm².​

• Matches real-world cases like sedimentation or Brownian motion.

• Differs from quadratic drag (½ρv²Cd A), which is dimensionless Cd.

Option Breakdown

This resolves competitive exam questions on drag coefficient units cgs, emphasizing Stokes flow fundamentals.