Question

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The conical shell of a ball mill is operated at a speed slightly higher than the critical speed.
Reason R: Critical speed of a ball is that rotational speed at which centrifuging occurs.
In light of the above statements, choose the correct answer from the options given below:

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is NOT the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Hint:

To ensure effective grinding, the operating speed of a ball mill must always be below its critical speed:
\[ N_{\text{operating}} \approx (0.65 \text{ to } 0.80) \cdot N_{\text{critical}} \]
At or above critical speed, centrifuging prevents any grinding action.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
A ball mill is a size-reduction machine consisting of a rotating hollow cylindrical or conical shell filled with steel or ceramic balls.
The grinding action is achieved as the balls are lifted by the rotating shell and then cascade or fall onto the feed material.
The rotational speed of the mill is a critical operating parameter that determines the grinding efficiency.

Step 2: Detailed Explanation:
Let us analyze both statements in detail:
- Assertion A: The critical speed of a ball mill is the rotational speed at which the centrifugal force acting on the grinding balls equals the gravitational force.
If the mill is operated at or above this critical speed, the balls cling to the inner wall of the shell due to centrifugal force and do not fall.
This state is known as "centrifuging."
Since the balls do not fall, no impact or grinding occurs, and the size-reduction process stops.
Therefore, a ball mill must be operated at a speed slightly lower than its critical speed (typically \( 65% \) to \( 80% \) of the critical speed) to ensure the balls cascade and grind the material effectively.
Thus, Assertion A is false.
- Reason R: The critical speed is defined mathematically by equating the centrifugal force to the gravitational force:
\[ m \cdot \omega_c^2 \cdot R = m \cdot g \]
At this rotational speed, the balls are held against the mill wall throughout the entire rotation, preventing them from falling.
This confirms that the critical speed is the speed at which centrifuging begins.
Thus, Reason R is true.
Since Assertion A is false and Reason R is true, option (D) is the correct choice.

Step 3: Final Answer:
Assertion A is false but Reason R is true.