Particle size analysis — pick the wrong statement:\nIdentify the incorrect statement regarding surface-area estimation, crusher capacity under choke feed, and mill charge motion terminology.

Introduction / Context:
Size analysis and comminution terminology can be confusing. Two common data presentations are cumulative and differential size distributions, each with strengths and limitations. Separately, choke feeding and mill charge motion concepts are frequent exam topics. This question asks you to spot the one incorrect or misleading statement among several commonly cited facts.

Given Data / Assumptions:

• Cumulative and differential analyses refer to the same underlying sieve or laser data.
• Crusher is operated in choke feed (chamber filled to ensure inter-particle crushing).
• Standard tumbling-mill motion terms apply.

Concept / Approach:
Differential analysis reports the mass in each size interval and is the standard basis for surface-area estimation, but it requires assuming a representative size within each interval (often the geometric mean). Cumulative analysis sums undersize and is excellent for visualising cut points, but deriving surface from a cumulative curve still implies an assumed size distribution within bins; it does not “avoid” the representative-size assumption. Thus, claiming cumulative analysis is preferred because it avoids that assumption is incorrect. The Gates–Gaudin–Schuhmann (GGS) cumulative plot against 1/d permits area-based surface estimates, choke feeding generally raises capacity (and fines) for suitable crushers, and “cascading”/“cataracting” definitions are standard.

Step-by-Step Solution:

Verification / Alternative check:
Texts derive specific surface from differential distributions by summing over size classes using class midpoints; cumulative plots are a reexpression and do not eliminate that need.

Why Other Options Are Wrong:

• (b): GGS plot relation to surface is standard.
• (c): Choke feeding can increase throughput for certain crusher types.
• (d): Motion terms are correctly defined.

Common Pitfalls:
Assuming a change of plotting style (cumulative vs differential) changes the underlying assumptions; it does not.

Final Answer:
Cumulative analysis is preferred over differential for surface area estimation because it avoids assuming “all particles in a size fraction are equal”, which differential analysis requires.