Find the moment of inertia of the system

Question

the position vectors of two point like object of mass 100kg and 200kg are (2,4,6)m and (3,5,7)m respectively.Find the moment of inertia of the system about Y- axis

Answer 1

m₁ = 100 kg, m₂ = 200 kg

 

r₁² = (2² + 6²)m² = 40 m², r₂² = (3² + 7²)m² = 58 m²

 

I = m₁r₁² + m₂r₂² = (100 kg)(40 m²) + (200 kg)(58 m²) = 15600 kg·m²