Three equal masses m are rigidly connected to each other by massless rods of length l forming an equilateral triangle, as shown in the figure. What is the ratio of the moment of inertia of the assembly for an axis through B compared with that for an axis through A (centroid). Both the axis are perpendicular to the plane of triangle.

Question

G1 Physics · Accepted Answer

For an equilateral triangle of three equal point masses, the centroid is at distance ℓ/√3 from each mass. Thus Iₐ=3m(ℓ²/3)=mℓ². About an axis through vertex B, one mass is on the axis and the other two are each at distance ℓ, so Iᵦ=2mℓ². Hence Iᵦ/Iₐ=2.