Where is the Center of Mass Located in a System of Two Unequal Rods?

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In a system of two unequal rods, where one rod is twice the weight of the other, the center of mass is not simply located at the midpoint. Instead, it is influenced by the weights and lengths of the rods. The center of mass can be calculated using the formula that considers the weighted average of their positions. For the given scenario, the center of mass would indeed be closer to the heavier rod, specifically around 2/3 of the way from the thinner end. Accurate calculations are essential to determine the precise location of the center of mass in such systems.
schaafde
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Given the picture in the attachment of two rods touching with them each being 17 inches long and one weighing double the weight of the other, would it make sense that the center of mass is 2/3 of the way down the picture from the thinner end? Or, am I going about this idea the wrong way?
 

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