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classical mechanics
Don't know the english terms so I'll try and explain simply. The twisting forces you get from the weight of the piece and it's length are equal. In the short piece you have to have a high weight, because the length is low. The second piece is the opposite.

That is correct.
Torque = force * lever arm (length)
force = mass (weight) * gravitational acceleration (constant)

When in balance the torque on both sides of the center of gravity is equal. When the lever arm (length) is different on both sides and the torque on both sides is equal then the mass must be different. The long arm has smaller mass, the shorter arm has a higher mass.

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