Concept:
Particle size can be measured by several methods, each based on a different physical principle. The Andreasen pipette is a sedimentation method, so we should recall what governs sedimentation.
Step 1: The Andreasen pipette works on the principle of settling (sedimentation) of particles in a fluid. Larger, heavier particles settle faster and smaller particles settle slower, exactly as described by Stokes' law. By withdrawing samples from a fixed depth at different times and weighing the solids, we work out the particle size distribution.
Step 2: The other options point to different instruments — change in electrical resistance is the principle of the Coulter counter, direct measurement is microscopy, and resistance to airflow relates to permeametry methods. Only the rate of settling describes the Andreasen pipette.
Answer: Option (1) — the Andreasen pipette is based on the rate of settling of particles in a fluid. (1)