A uniform wire frame ABC is in the shape of an equilateral triangle in xy-plane. The centroid is the origin.
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An equilateral triangle wire frame ABC has its centroid at the origin. The center of mass (COM) of the entire frame is at the origin. When one side is removed, the COM of the remaining two sides shifts away from the missing mass.
Let the mass of each side be . The COM coordinates for a side are at its midpoint. For a triangle symmetric about the origin, if side AB (base) is removed, the COM of sides AC and BC shifts upward into the second quadrant. If side AC is removed, the COM of sides AB and BC shifts into the first quadrant. If side BC is removed, the COM shifts into the fourth quadrant.
Final Answer: The correct statements are: If AB is removed, the COM is in the second quadrant; If AC is removed, the COM is in the first quadrant; If BC is removed, the COM is in the fourth quadrant.