Add 200 lb payload at 60 inches to the original 1,200 lb at 24 and 1,000 lb at 14; total weight 1,700; CG ≈ ?

Add 200 lb payload at 60 inches to the original 1,200 lb at 24 and 1,000 lb at 14; total weight 1,700; CG ≈ ?

• A. 21.0 inches
• B. 22.0 inches
• C. 21.2 inches
• D. 20.5 inches

Answer: (C)

Center of gravity is found by taking the weighted average of all load positions. In practice, you multiply each load by its lever arm, sum those moments, and divide by the total weight. For the given loads: 1,200 lb at 24 inches, 1,000 lb at 14 inches, and a 200-lb payload at 60 inches. The moments are 1,200×24 = 28,800 in-lb, 1,000×14 = 14,000 in-lb, and 200×60 = 12,000 in-lb. The total moment is 28,800 + 14,000 + 12,000 = 54,800 in-lb. The total weight is 1,200 + 1,000 + 200 = 2,400 lb. Therefore, CG ≈ 54,800 / 2,400 ≈ 22.83 inches from the datum. So the CG sits about 22.8 inches from the reference point. The option closest to that value would be the one around 22 inches. If the provided answer states 21.2 inches, note that with these exact weights and distances, the calculated CG is about 22.8 inches; a mismatch like that usually means a misprint or a different total weight or arm data in the problem.

Center of gravity is found by taking the weighted average of all load positions. In practice, you multiply each load by its lever arm, sum those moments, and divide by the total weight.

For the given loads: 1,200 lb at 24 inches, 1,000 lb at 14 inches, and a 200-lb payload at 60 inches. The moments are 1,200×24 = 28,800 in-lb, 1,000×14 = 14,000 in-lb, and 200×60 = 12,000 in-lb. The total moment is 28,800 + 14,000 + 12,000 = 54,800 in-lb. The total weight is 1,200 + 1,000 + 200 = 2,400 lb. Therefore, CG ≈ 54,800 / 2,400 ≈ 22.83 inches from the datum.

So the CG sits about 22.8 inches from the reference point. The option closest to that value would be the one around 22 inches. If the provided answer states 21.2 inches, note that with these exact weights and distances, the calculated CG is about 22.8 inches; a mismatch like that usually means a misprint or a different total weight or arm data in the problem.