Under the same line, several topological indices have been investigated within the ER model, employing computational or analytical approaches ; since, for instance, comprehensive knowledge of various indices pertaining to the model could function as indicators of whether a network conforms to the Erdős-Rényi random graph model. Similarly, the generalized Randić index has been scrutinized across various random models . Moreover, as points of intersection, the generalized Randić index has been examined within the ER model . Specifically, the generalized Randić index has been employed to estimate graph robustness and, at the same time, ER graphs have served as valuable benchmarks for evaluating graph robustness . This measure, which indicates a graph's capacity to sustain connectivity amidst node and edge loss, aids in examining the resilience of various systems. Inspired by the foregoing, the objective of this paper is to examine the asymptotic properties of the generalized Randić index in both dense and sparse scenarios through the application of the second moment method. Additionally, it aims to corroborate the empirical findings of previous studies and to show consistency with the theoretical results derived through different approaches.