By the perpendicular axis theorem, the moment of inertia about the center of mass (assuming the given orthogonal axes intersect at CM) and perpendicular to the plane is I_CM = Ix + Iy = 3 kg m² + 4 kg m² = 7 kg m². By the parallel axis theorem, the moment of inertia I about a parallel axis perpendicular to the plane and at a distance d = 0.5 m from CM is I = I_CM + m d².
A planar, irregular shaped object has a mass of 2 kg. Its moment of inertia along the two orthogonal axes in the plane of the object are 3 kg m² and 4 kg m², respectively. The moment of inertia of the object along an axis perpendicular to the plane and passing through a point 0·5 m away from its centre of mass is represented by I. Which one among the following is the correct value of I ?
Asked in UPSC Geoscientist 2024 · Topic: Mechanics (Rotational Dynamics and Moment of Inertia)
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