---
title: "Centre of gravity versus centroid"
subject: "Strength of Materials"
chapter: 2
key: "semester_3/strength_of_materials:centroid-vs-cg"
source: https://www.bctengineer.com/q/semester_3/strength_of_materials/centroid-vs-cg
site: BCT Engineering
---

# Centre of gravity versus centroid

Strength of Materials · Chapter 2: Geometrical Properties of Sections

- Asked in: 2081 Baisakh, 2 marks
- Video: [“Centroid vs Center of Mass vs Center of Gravity — Know the Difference!”](https://www.youtube.com/watch?v=qyYbrhH8e4U) — TotalBlend
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/strength_of_materials/centroid-vs-cg
- Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-2

## Question

Differentiate between centre of gravity (CG) and centroid.

## Short answer

Centre of gravity is the point where the entire weight of a body acts, depending on mass distribution and gravity. Centroid is the geometric centre of an area or volume, independent of material. They coincide for a homogeneous body in uniform gravity.

## Answer

| Point | Centre of gravity (CG) | Centroid |
|---|---|---|
| Meaning | The point through which the **weight** of the body acts | The **geometric centre** of an area, line or volume |
| Depends on | Mass distribution and gravity | Shape only |
| Applies to | 3-D bodies (solid, with weight) | Plane areas, lines, volumes (geometric figures) |
| Material | Depends on density of each part | Independent of material |
| Coincidence | Coincides with the centroid when the body is homogeneous (uniform density) and gravity is uniform | Same as CG for a homogeneous body |
| Formula | $\bar x = \dfrac{\sum W_ix_i}{\sum W_i}$ | $\bar x = \dfrac{\sum A_ix_i}{\sum A_i}$ |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the basic difference between centre of gravity and centroid?
   A. CG is the point where the weight acts; the centroid is the geometric centre of a shape
   B. CG is for areas only; centroid is for bodies only
   C. They are always different points
   D. CG depends only on shape
   Answer: A. CG is the point through which the weight of a body acts, whereas the centroid is purely the geometric centre of a line, area or volume. (Key point: Meaning)

2. On which factor does the centroid NOT depend?
   A. The shape
   B. The material density
   C. The dimensions
   D. The geometry of the area
   Answer: B. The centroid depends only on shape, independent of the material, while the CG depends on the density distribution. (Key point: Dependence)

3. When do the CG and the centroid coincide?
   A. Never
   B. When the body is homogeneous and gravity is uniform
   C. When the body is very heavy
   D. Only for circular bodies
   Answer: B. For uniform density and uniform gravity, weight is proportional to volume, so the weighted CG formula reduces to the geometric centroid. (Key point: When they coincide)

## Related in Strength of Materials

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