Centre of gravity of a rectangle — location statement The centre of gravity (centroid) of a uniform rectangle lies at the intersection point of its two diagonals.

Introduction / Context:The centroid (centre of gravity for uniform density) of standard shapes is fundamental in structural analysis, bending, and area-moment calculations. For rectangles, the centroid is famously at the intersection of diagonals.

Given Data / Assumptions:

• Uniform thickness and density.
• Planar, axis-aligned rectangle of width b and height h.
• No cut-outs or holes.

Concept / Approach:By symmetry, the centroid must lie midway between parallel sides. Therefore, it is located at coordinates (b/2, h/2) measured from a corner, which is exactly where the diagonals intersect.

Step-by-Step Solution:

Verification / Alternative check:Apply the first-moment-of-area definition: x̄ = (∫ x dA)/A and ȳ = (∫ y dA)/A. For a uniform rectangle, both evaluate to mid-spans.

Why Other Options Are Wrong:

• Disagree / unless square: The result holds for any rectangle, not only squares.
• Density varies linearly: The statement assumes uniform density; non-uniformity would shift the centroid.

Common Pitfalls:Confusing “centre” with any geometric center point even when cut-outs exist; the centroid changes if holes or non-uniform density are present.

Final Answer:Agree