# Plane Center of Gravity

Introduction to plane centre of gravity:

The force with which the earth attracts any other objects towards its centre is called the gravity or the force of gravity. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped. Actually, this force is not acting on the whole body, this act only at the single point. This single point is called the centre of gravity. The force of gravity always acts on the centre of gravity of the body. Here we discuss what is centre of gravity and how we calculate it for a plane body.

Plane Centre of Gravity

The centre of gravity is the point on the body or inside the body at which the earth exerts a force of gravity. Any extended body can be assumed to be made by the small particles. The earth attracts each of these particles by a force, which equals to the weight of the respective particle. Thus a large number of forces of magnitudes m1g, m2g, m3g, mng, etc., act at different points of the body.

Here m1, m2, m3,…,mn, etc, are the masses of the particles. Assuming that these forces are parallel, their sum is

m1g, m2g, m3g,…, mng = Mg, where M is the mass of the whole body.

It turns out that there is a special point C in the body such that if a single force Mg acts at this point in the downward direction, it produces the same effect on the body as produced by all the forces m1g, m2g, m3g,…, mng, etc., taken together. This point is called the centre of gravity of the body. The centre of gravity of a body is a point where the entire weight of the body may be assumed to act. It is easy to find that the centre of gravity of a body having uniform density and simple geometrical shape. For example, the centre of gravity of a uniform rod is its midpoint, which of a disc or a sphere is at its centre and so on.

Conclusion for the Plane Centre of Gravity:

When we are studying about the effect of gravity on a body, the whole body may be assumed to be concentrated at its centre of gravity. Be careful in making use of this fact. This equivalence is valid only for the studying the effect of gravity on the body.

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