Which of the following statements correctly describes the calculation to obtain CG when weights are at multiple stations?

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Multiple Choice

Which of the following statements correctly describes the calculation to obtain CG when weights are at multiple stations?

Explanation:
When weights are at multiple stations, the center of gravity is the distance from the reference datum where the entire aircraft’s weight could be considered to act. You determine it by using moments. A moment is produced by each weight times its arm (the distance from the datum). Add up all those individual moments to get the total moment. Then divide that total moment by the sum of all weights (the total weight). The result is the CG location. In other words, CG equals total moment divided by total weight. This reflects the idea that the CG is the weighted average position of all the weights. For example, if you have two weights: one of 100 units at an arm of 5 units, and another of 50 units at an arm of 15 units, the total moment is 100×5 + 50×15 = 500 + 750 = 1250. The total weight is 150. The CG is 1250 ÷ 150 ≈ 8.33 units from the datum. Dividing total weight by total moment would give an inverse quantity with units of 1/length, not a distance. Averaging weights alone ignores how far each weight is from the datum, so it doesn’t locate CG.

When weights are at multiple stations, the center of gravity is the distance from the reference datum where the entire aircraft’s weight could be considered to act. You determine it by using moments.

A moment is produced by each weight times its arm (the distance from the datum). Add up all those individual moments to get the total moment. Then divide that total moment by the sum of all weights (the total weight). The result is the CG location.

In other words, CG equals total moment divided by total weight. This reflects the idea that the CG is the weighted average position of all the weights.

For example, if you have two weights: one of 100 units at an arm of 5 units, and another of 50 units at an arm of 15 units, the total moment is 100×5 + 50×15 = 500 + 750 = 1250. The total weight is 150. The CG is 1250 ÷ 150 ≈ 8.33 units from the datum.

Dividing total weight by total moment would give an inverse quantity with units of 1/length, not a distance. Averaging weights alone ignores how far each weight is from the datum, so it doesn’t locate CG.

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