ANS:A - less than

The operating speed of a ball mill should be at least equal to the critical speed.

Explanation:

• Critical Speed: The critical speed NcN_{\text{c}}Nc​ of a ball mill is defined as the rotational speed at which the centrifugal force due to the rotation of the mill shell equals the gravitational force acting on the grinding media (balls) and the material being ground.
• Significance of Critical Speed: Operating the ball mill at or above the critical speed ensures that the grinding media (balls) are lifted to the maximum height and then cascaded down, which enhances grinding efficiency.
• Relation to Operating Speed:
  • Equal to: Operating at the critical speed NcN_{\text{c}}Nc​ or slightly above ensures optimal grinding action and efficiency.
  • Less than: Operating below the critical speed may result in ineffective grinding and reduced throughput.
  • Much more than: Operating significantly above the critical speed can lead to excessive wear of the mill shell and grinding media, as well as reduced efficiency.
  • Slightly more than: This option is less precise compared to "at least equal to" and does not accurately reflect the critical speed requirement.