Question

A body having its centre of mass at the origin has three of its particles at (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

(d) cannot be deduced with this information.

I_x = m₂a² + m₃a² = 0.20 ...(i)
I_y = m₁a² + m₃a² = 0.20 ...(ii)
I_z = m₁a² + m₂a² ...(iii)
We have three equations and four variables. So, I_z cannot be deduced with the given information.