Two thin rods, each of mass m and length ℓ, lie along the x-axis and y-axis with their centres at the origin. What is the moment of inertia of the system about the line x = y?
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Question

Two thin rods, each of mass m and length ℓ, lie along the x-axis and y-axis with their centres at the origin. What is the moment of inertia of the system about the line x = y?

G1 Physics · Accepted Answer

Each rod has moment of inertia mℓ²/12 about an axis through its centre perpendicular to the rod. The line x=y makes 45° with each rod, so for one rod I=(mℓ²/12)sin²45°=mℓ²/24. For two rods, I=2(mℓ²/24)=mℓ²/12. Hence option B.