Definition — what is a centroid? In engineering mechanics of areas, the term “centroid” refers to which of the following?

Introduction / Context:
The centroid is a geometric property of an area and is fundamental when computing bending stresses, shear flow, and deflections. It is often confused with the centre of gravity (C.G.).

Given Data / Assumptions:

• We consider plane areas (laminae) of uniform thickness and material, unless otherwise stated.
• Gravitational field is uniform when comparing centroid to C.G.

Concept / Approach:
The centroid is the point where the first moments of area about any axis through that point are zero. For a thin homogeneous lamina in a uniform gravitational field, the centroid coincides with the centre of gravity. However, if density varies or the field is non-uniform, the C.G. may shift while the centroid, being purely geometric, does not.

Step-by-Step Solution:

Verification / Alternative check:
For symmetric shapes (e.g., rectangle), centroid lies at the intersection of symmetry axes, confirming the geometric definition.

Why Other Options Are Wrong:

• Same as C.G. always: Only true under uniform density and field; not universally true.
• Point of suspension / resultant of forces / instantaneous centre: These are dynamics/statics notions, not the area property.

Common Pitfalls:
Using “centroid” and “centre of gravity” interchangeably without checking density and field assumptions.

Final Answer:
The geometric centre of area of a plane figure (point where first moments of area about any axis through it are zero).