Ball mill operation: which statement is correct for selecting ball size and operating speed?

Introduction / Context:
Ball mills reduce particle size through impact and attrition between tumbling balls and the charge. Matching media size and speed to feed size and desired product is central to efficient comminution.

Given Data / Assumptions:

• Larger balls deliver higher impact energy suited to coarse particles.
• Critical speed defines the onset of centrifuging; operation is normally at a fraction of critical (e.g., 65–80%).
• Fine feeds benefit from smaller balls for increased surface contact and attrition.

Concept / Approach:
Impact energy scales with ball mass and velocity. Coarser particles need larger balls to fracture effectively. Operating above critical speed causes balls to stick to the shell (centrifuging), reducing grinding action; thus mills run below critical speed. For fine grinding, smaller media increases contact frequency and surface area.

Step-by-Step Solution:
Relate particle size to required impact: coarse → larger balls.Reject the claim that fine feed needs larger balls; inverse is true.Reject running above critical speed; typical operation is below.

Verification / Alternative check:
Design handbooks recommend graded charges with larger top sizes for coarser feeds and lower mill speeds as a fraction of critical.

Why Other Options Are Wrong:
(b) contradicts standard practice; (c) contradicts the definition of critical speed; (d) is invalid because (a) is correct.

Common Pitfalls:
Ignoring mixed-media charges; single-size charges are less efficient across wide feed distributions.

Final Answer:
Coarse feed requires a larger ball size.