Two boxes weighing 10 pounds and 5 pounds are placed in an airplane so that their distances aft from the CG are 4 feet and 2 feet respectively. How far forward of the CG should a third box weighing 20 pounds be placed so that the CG will not be changed?

• A. 2 feet
• B. 2.5 feet
• C. 3 feet
• D. 4 feet

Answer: (B)

Center of gravity is the balance point of all weights, found as the weighted average of their positions. Here, the two known boxes create a total moment about the CG of 10 lb at 4 ft plus 5 lb at 2 ft, which is 40 + 10 = 50 ft-lb aft.

To keep the CG at the same point when adding a third box of 20 lb, place it in front of the CG by a distance x, giving a moment of -20x about the CG (negative because it’s forward). Set the total moment to zero to keep the CG unchanged: 50 - 20x = 0, so x = 50/20 = 2.5 ft.

Therefore, place the 20-pound box 2.5 feet forward of the CG. If placed less or more, the net moment would not be zero, shifting the CG aft or forward accordingly.