The center of gravity (center of mass), is the point at which the whole weight of a body is considered to act.

How to find the center of gravity for irregular objects

Activity

Here is an activity to determine the center of mass of a plane lamina.

You will need:

An irregularly shaped piece of flat cardboard, lamina (See pic below)
A pin
A cork or other soft material such as  Styrofoam
A plum-bob, string with a weight at the end
A place to clamp the cork. If in a lab use a retort stand, if at home use two books to secure the cork

(Download lamina template)

Method:

Stick the lamina through with the pin close to one edge, (point A)
Stick the pin into the cork and clamp the cork using the retort stand or secure with books
Ensure that the lamina hangs freely in the vertical direction
Tie the plumb-bob onto the end of the pin so that it hangs in front of the lamina
Ensure the plum-bob and lamina come to rest
Mark the opposite end of the lamina where the plumb-bob touches, (point B)
Dismount the lamina and draw a line connecting the point of suspension to the opposite end i.e connect point A to point B
Repeat this procedure twice using different edges as the starting point
Mark the point of intersection of the three lines
This point is the center of gravity

Try to balance the lamina at its center of gravity on your finger. Did it work?

These images are only for illustration purposes only

Here is a video showing the process.

How to find the center of gravity for regular objects

The center of gravity of objects that have uniform thickness and density is usually at its geometrical center. Examples of these are

The black dot shows the location of the center of gravity. It is not always physically located on the object as is the case of a ring with a hollow center such as a doughnut.

Credit
Header image:
By APN MJM – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=18108175