Suppose two bodies possess an identical geometrical shape, with the...

The moment of inertia of a body is given by $I = \int r^2 dm = \int r^2 \rho dV$, where $\rho$ is the density of the material and $dV$ is the volume element.

Since both bodies have identical geometrical shapes, the integral $\int r^2 dV$ is the same for both.

Therefore, the moment of inertia is directly proportional to the density of the material, $I \propto \rho$.

The density of aluminium is less than the density of iron, $\rho_{Al} < \rho_{Fe}$.

Hence, the moment of inertia of the aluminium body is less than that of the iron body, which gives $I_1 < I_2$.