A moment calculation: two weights, 900 lb at 15 inches and 600 lb at 40 inches. What is the center of gravity (inches)?

A moment calculation: two weights, 900 lb at 15 inches and 600 lb at 40 inches. What is the center of gravity (inches)?

• A. 25 inches
• B. 15 inches
• C. 40 inches
• D. 37 inches

Answer: (A)

Center of gravity is found by weighting each position by its load and dividing by the total load. Multiply each distance by its weight to get moments, sum them, then divide by the total weight. Here, 900 lb at 15 inches gives 13,500 in-lb of moment, and 600 lb at 40 inches gives 24,000 in-lb. Total moment = 37,500 in-lb. Total weight = 900 + 600 = 1,500 lb. Center of gravity = 37,500 / 1,500 = 25 inches. So the CG lies between the two locations, closer to the heavier weight at 15 inches, which matches the weighted influence. The other numbers would place the CG at a weight’s exact position or farther toward 40 inches, not reflecting the combined effect of both loads.

Center of gravity is found by weighting each position by its load and dividing by the total load. Multiply each distance by its weight to get moments, sum them, then divide by the total weight.

Here, 900 lb at 15 inches gives 13,500 in-lb of moment, and 600 lb at 40 inches gives 24,000 in-lb. Total moment = 37,500 in-lb. Total weight = 900 + 600 = 1,500 lb. Center of gravity = 37,500 / 1,500 = 25 inches.

So the CG lies between the two locations, closer to the heavier weight at 15 inches, which matches the weighted influence. The other numbers would place the CG at a weight’s exact position or farther toward 40 inches, not reflecting the combined effect of both loads.