Question

A body having its centre of mass at the origin has three of its particles $(a, 0, 0), (0, a, 0), (0, 0, a)$. The moments of inertia of the body about the X and Y axes are 0.20 kg-m² each. The moment of inertia about the Z-axis :

• A. Is 0.20 kg-m²
• B. Is 0.40 kg-m²
• C. Is 0.20$\sqrt{2}$ kg-m²
• D. Cannot be deduced with this information

Answer 1

Answer: (A)

Is 0.20 kg-m²

Answer 2

The given particle positions $(a, 0, 0)$, $(0, a, 0)$, and $(0, 0, a)$ exhibit symmetry with respect to cyclic permutation of the axes. Coupled with the fact that the moments of inertia about the X and Y axes are equal ($I_x = I_y = 0.20 \, \text{kg-m}^2$), this strongly suggests that the body possesses symmetry such that the moment of inertia about the Z-axis is also equal to these values. This symmetry is characteristic of bodies with cubic symmetry about the origin when the axes are principal axes. Therefore, $I_z = I_x = I_y$.