Centre Of Gravity - Byju's

Determining the Centre of Gravity for Symmetrical Bodies

For simple shaped object, the centre of gravity can be determined by the following ways:

1. When we balance an object with the help of a string or an edge, the point at which the object balances is the centre of gravity.
2. Another simple physical procedure employed to determine the centre of gravity is as follows:

Suspending the plate given in the figure by attaching a cord to point A and then by attaching the cord at point C, the centre of gravity of the plate can be located.

The line AD is vertical when the plate is suspended from A; likewise, the line CE is vertical when suspended from C. The centre of gravity of the plate lies at the intersection of AD and CE. When an object is suspended from any single point, its centre of gravity lies directly beneath that point.

Determining the Centre of Gravity for Asymmetrical Bodies

We make use of calculus to determine the centre of gravity when the mass is not distributed uniformly. We denote the integration of a continuous function with respect to weight using the symbol S dw. Then, the centre of gravity is determined as follows:

\(\begin{array}{l}cg\times W=SxdW\end{array} \)

Here, x is the distance from a reference line, dw is an increment of weight, and W is the total weight of the object.

We know that

\(\begin{array}{l}W = mg\end{array} \)

But, the mass of an object is equal to

\(\begin{array}{l}m=\rho V\end{array} \)

Combining both the equations, we get

\(\begin{array}{l}W=g\rho V\end{array} \)

Solving,

\(\begin{array}{l}dW=g\rho dV\end{array} \) \(\begin{array}{l}dW=g*\rho(x,y,z)* dxdydz\end{array} \)

If we have a functional form of the mass distribution, we can solve the equation for the centre of gravity.

\(\begin{array}{l}cg * W = g * SSS x * \rho (x,y,z) dx dy dz\end{array} \)

SSS in the equation indicates a triple integral over dx. dy. and dz.

Difference Between Centre of Mass and Centre of Gravity

It is common to assume the centre of mass and the centre of gravity to be the same, but this is not the case.

The centre of mass is a point at which mass distribution is equal in all directions, and it doesn’t depend upon the gravitational field. The centre of gravity is a point in an object where the distribution of weight is equal in all directions, and it does depend on the gravitational field.

However, an object’s centre of mass and centre of gravity lies at the same point in a uniform gravitational field.

In the above figure, the object on the left is in a uniform gravitational field and has an overlapping centre of gravity and mass. For the object on the right, the gravitational field is stronger towards its base, and the centre of gravity is below the centre of mass.

How can a ring be balanced if its centre of gravity lies outside?

The centre of gravity of a uniform circular ring does not lie in its centre but at its geometric centre. Although it lies outside the mass, the centre of gravity of a circular ring balances itself when placed on another object, as shown in the figure. The gravitational force acts through the supporting object.

Frequently Asked Questions on Centre of Gravity

Q1

Who discovered the centre of gravity?

Archimedes of Syracuse discovered the centre of gravity.

Q2

How does the Centre of gravity affect the balance?

The centre of gravity affects the stability of objects. The lower the centre of gravity (G) is, the more stable the object. The higher it is, the more likely the object is to topple over if it is pushed. Racing cars have shallow centres of gravity so that they can corner rapidly without turning over.

Q3

Why is the centre of gravity important?

The Centre of gravity vastly simplifies calculations involving gravitation and dynamics to treat the mass of an object as if it is concentrated at one point.

Q4

Where is the centre of gravity in a human body?

In an anatomical position, the centre of gravity lies approximately anterior to the second sacral vertebra. However, since human beings do not remain fixed in the anatomical position, the precise location of the COG changes constantly with every new position of the body and limbs.

Q5

How does centre of gravity affect stability

The position of the centre of gravity of an object affects its stability. The lower the centre of gravity (G) is, the more stable the object. The higher it is, the more likely the object is to topple over if it is pushed.

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