Physics Question from JEE Main 2023 · 6 April, Shift 1

Two identical solid spheres each of mass $2 \, \text{kg}$ and radii $10 \, \text{cm}$ are fixed at the ends of a light rod. The separation between the centres of the spheres is $40 \, \text{cm}$. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is _____ $\times 10^{-3} \, \text{kg}\cdot\text{m}^2$.