Centre of gravity (definition and meaning): For a homogeneous rigid body, the centre of gravity is the point at which the entire ____ is considered to act.

Introduction / Context:
The centre of gravity (CG) is a foundational concept in statics and dynamics. It allows engineers to replace the distributed gravitational forces on a body by a single resultant acting at a specific point for equilibrium and motion analysis.

Given Data / Assumptions:

• Rigid body with uniform gravitational field.
• Homogeneous body means constant density, but the definition does not require homogeneity.
• We are interested in the definition—where the resultant weight acts.

Concept / Approach:
The CG is the point at which the resultant of gravitational forces (body weight) is taken to act. For uniform gravity fields, the centre of gravity coincides with the centre of mass. This point simplifies calculations of balance, support reactions, and rotational dynamics under gravity.

Step-by-Step Solution:

Verification / Alternative check:
For symmetric uniform bodies, G lies at the geometric centre (e.g., the centroid for laminae). Lever-balance experiments also identify the point where net moment of weight is zero in all orientations.

Why Other Options Are Wrong:

• Volume/area concentrated (a or b): useful for centroid definitions of volume or area, but CG specifically refers to weight (force) concentration.
• “All the above” mixes geometric centroids with gravitational resultant, which is imprecise.

Common Pitfalls:
Confusing centre of mass, centroid, and centre of gravity—these coincide only under uniform gravity and homogeneity.

Final Answer:
weight of the body