For a composite area, the centroidal x-coordinate bar x of the composite is:

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Mechanical Engineering QUESTION #2550

Question 1

For a composite area, the centroidal x-coordinate \(\bar{x}\) of the composite is:

\(\bar{x}=\frac{\sum A_i}{\sum A_i\bar{x}_i}\)
\(\bar{x}=\frac{\sum A_i\bar{x}_i}{\sum A_i}\)✔️
\(\bar{x}=\frac{1}{n}\sum\bar{x}_i\)
\(\bar{x}=\sum A_i\bar{x}_i\)

Correct Answer Explanation

The centroid is found by dividing the first moment of the entire area by the total area: \(\bar{x}=\frac{\sum A_i\bar{x}_i}{A_{total}}\). Simple arithmetic mean of centroids (option 3) is wrong because it does not account for area weighting.

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