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Grab a pin, a pendulum (weight on the end of a piece of string), a ruler and pencil. Push the pin through the object and attache the pendulum to the pin. Make sure that the irregular object hangs freely on the pin. Allow pendulum and object to settle. Carefully mark where the pendulum crosses the bottom edge of your object, then join that mark with the original hole using a ruler.

If you repeat this experiment the lines should all cross at the cengre of gravity because that will always come to rest under the pin.

This assumes that the flatness is uniform.

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