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A uniform meter rule has its center of gravity at its midpoint, which is the 50 cm mark. When pivoted at this point, the weight of the rule acts through the pivot, producing no torque. Additionally, the rule is symmetric, so any mass placed at equal distances on either side would balance. The primary reason it balances at 50 cm is that the distances (and hence the lever arms) on both sides are equal when considering the rule's own weight distribution, so the moments are balanced.