Question

Which of the following statements are associated with the complete dynamic balancing of rotating systems?
I. Resultant couple due to all inertia forces is zero
II. Support reactions due to forces are zero but not due to couples
III. The system is automatically statically balanced
IV. Centre of masses of the system lies on the axis of rotation

• A. I, II, III and IV
• B. I, II and III only
• C. II, III and IV only
• D. I, III and IV only

Hint:

Remember the absolute hierarchy of balancing rules: - Dynamic Balancing $\implies$ Static Balancing (Always). - Static Balancing $\centernot\implies$ Dynamic Balancing. - Complete dynamic balance means Net Force = 0 AND Net Couple = 0, resulting in zero dynamic bearing reactions.

Answer 1

The Correct Option is D

The question asks about the statements associated with the complete dynamic balancing of rotating systems. To determine the correct answer, let's evaluate each statement:

1. Statement I: Resultant couple due to all inertia forces is zero
   • For a system to be dynamically balanced, the resultant couple (moment) due to all inertia forces must indeed be zero. This ensures there's no unbalanced torque that can cause vibration and stress in the system.
   • This statement is correct.
2. Statement II: Support reactions due to forces are zero but not due to couples
   • In a completely dynamically balanced system, it is important that both net forces and net moments (couples) are balanced. This statement suggests that only the net force is balanced and the couple is not, which does not align with the concept of complete dynamic balancing.
   • This statement is incorrect.
3. Statement III: The system is automatically statically balanced
   • If a system is dynamically balanced, it implies that the system is also statically balanced because the conditions required for static balance are a subset of those for dynamic balance.
   • This statement is correct.
4. Statement IV: Center of masses of the system lies on the axis of rotation
   • For dynamic balance, it is essential that the center of mass of the rotating components lies on the axis of rotation. This ensures that rotation does not cause any centrifugal forces that lead to vibration.
   • This statement is correct.

Based on the analysis of the statements:

• I, III, and IV are true and aligned with the principles of complete dynamic balancing.
• II is incorrect as it contradicts the condition needed for complete dynamic balancing.

Thus, the correct answer is the option with I, III, and IV only.