Centre of Gravity
The centre of gravity (C.G.) of a body is the point about which the algebraic sum of moments of weights of all the particles constituting the body is zero.
Key Idea: The entire weight of a body can be considered to act at a single point — its centre of gravity.
Concept Explanation
- A body consists of many small particles having weights w₁, w₂, w₃, …
- Since the Earth is very large, all gravitational forces acting on these particles are parallel and downward.
- These forces can be replaced by a single force:
W = w₁ + w₂ + w₃ + … - This total weight acts at a point G, where:
Sum of moments = 0 - This point G is called the Centre of Gravity.
Important: A body behaves as if its entire weight is concentrated at its centre of gravity.
Important Notes
-
Depends on Shape:
The position of C.G. depends on how mass is distributed.
Example:- Straight wire → C.G. at middle
- Same wire bent into circle → C.G. at centre
-
May lie outside the body:
Example: Ring or hollow sphere → C.G. at centre (empty space) -
Point particle concept:
A body can be treated as a point mass located at its C.G.
Centre of Gravity of Common Objects
| Object | Position of C.G. |
|---|---|
| Rod | Mid-point |
| Circular Disc | Geometric centre |
| Sphere (solid/hollow) | Geometric centre |
| Cylinder | Mid-point on axis |
| Solid Cone | h/4 from base |
| Hollow Cone | h/3 from base |
| Circular Ring | Centre |
| Triangular Lamina | Intersection of medians |
| Square / Rectangle / Parallelogram / Rhombus | Intersection of diagonals |
🎯 Teaching Tip
Ask students:
👉 “Why does a ring balance at a point where there is no material?”
This builds strong conceptual understanding of centre of gravity.
