Analogs of the Pólya–Szegő and Macai inequalities for the Euclidean moment of inertia of a convex domain

In this paper, we obtain two-sided estimates for the Euclidean moment of inertia $\mathrm{I}_{2}(G) $ of a convex domain $G$ on the plane in terms of geometric characteristics of this domain similar to the Pólya–Szegő and Makai inequalities for the torsional rigidity.