If the given weights are A = 100, B = 200, and C = 200, how far must weight B be shifted to obtain a new CG of 50?

• A. 45 inches left
• B. 50 inches left
• C. 55 inches left
• D. 60 inches left

Answer: (C)

To determine how far weight B must be shifted to achieve a new center of gravity (CG) of 50 inches, we need to apply the principle of moments, which states that the sum of the moments about the center of gravity must equal zero in a static system.

Let's label the distances of each weight from a reference point (usually the leftmost point) as follows:

• Weight A (100 lbs) is at distance xA

• Weight B (200 lbs) is at distance xB

• Weight C (200 lbs) is at distance xC

The original CG can be found using the formula:

[

CG_{\text{original}} = \frac{(A \times xA) + (B \times xB) + (C \times xC)}{A + B + C}

]

Assuming we arbitrarily start with weight A at distance 0, weight B can be placed at 100 inches, and weight C at 200 inches. Thus, we calculate the original CG:

[

CG_{\text{original}} = \frac{(100 \times 0) + (200 \times 100) + (200 \times 200)}{100 + 200 +