Which of the following statements are associated with complete dynamic balancing of rotating systems? 1. Resultant couple due to all inertia forces is zero. 2. Support reactions due to forces are zero but not due to couples. 3. The system is automatically statically balanced. 4. Centre of masses of the system lies on the axis of rotation.

Which of the following statements are associated with complete dynamic balancing of rotating systems? 1. Resultant couple due to all inertia forces is zero. 2. Support reactions due to forces are zero but not due to couples. 3. The system is automatically statically balanced. 4. Centre of masses of the system lies on the axis of rotation. Correct Answer 1, 3 and 4 only

Support reactions due to forces & couple both need to be zero.

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According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through center of gravity (i.e. $$I$$P) is given by (where, A = Area of the section, $$I$$G = Moment of inertia of the section about an axis passing through its C.G. and h = Distance between C.G. and the parallel axis.)
According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through center of gravity (i.e. $${I_{\text{P}}}$$) is given by (where, A = Area of the section, $${I_{\text{G}}}$$ = Moment of inertia of the section about an axis passing through its C.G. and h = Distance between C.G. and the parallel axis.)