An object is made up of three masses connected by massless rods of fixed length. Mass A is located at (30.0 cm, 0 cm) and has a mass of 250 grams, mass B is located at (0 cm, 30.0 cm) and has a mass of 350 grams, mass C is located at (-30.0 cm, 0 cm) and has a mass of 450 grams. What is the moment of inertia of this object about an axis perpendicular to the x-y plane and passing through the origin? A) 0.0945 kg m² B) 0.315 kg m² C) 0.185 kg m² D) 0.0135 kg m² E) 0.0450 kg m²

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Quizplus · Accepted Answer

The moment of inertia of the object about an axis perpendicular to the x-y plane and passing through the origin is given by:$$I = mA^2 + mB^2 + mC^2$$where m is the mass of each object and A, B, and C are the distances from the axis to the center of mass of each object.In this case, we have:$$mA = 250 g = 0.25 kg$$$$A = 30.0 cm = 0.3 m$$$$mB = 350 g = 0.35 kg$$$$B = 30.0 cm = 0.3 m$$$$mC = 450 g = 0.45 kg$$$$C = 30.0 cm = 0.3 m$$So, the moment of inertia is:$$I = (0.25 kg)(0.3 m)^2 + (0.35 kg)(0.3 m)^2 + (0.45 kg)(0.3 m)^2$$$$I = 0.0945 kg m^2$$Therefore, the correct answer is A.

An Object Is Made Up of Three Masses Connected by Massless