How is the center of gravity determined from moments and weights?

• A. Total weight / total moment
• B. Sum of moments
• C. Total moment / total weight
• D. Center of gravity is independent of weight and moment

Answer: (C)

Center of gravity is the balance point of all weights, found by the weighted average position of those weights. Each weight creates a moment about a reference point equal to its weight times its distance from that point. If you sum all those moments, you get the total moment. To locate the center of gravity along that axis, you divide the total moment by the total weight. This leaves a distance, which is where the center of gravity lies.

In formula form, CG location along an axis = sum(weight_i × distance_i) / sum(weight_i). If you’re working in three dimensions, compute this for each axis (x, y, z) separately.

Why this method works: dividing the total moment by the total weight collapses the distribution of weights into a single point where the resultant weight would act, giving the proper balance point. The other ideas aren’t correct because a total weight divided by a total moment doesn’t yield a distance, and simply summing moments gives just the total moment, not the location. The center of gravity does depend on how the weights are arranged.