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We know that the angular momentum $L=I\omega$ of the Earth remains constant as there are no external torques acting on the Earth. On the other hand, due to the Earth expansion (that is, increase in radius), we know that there should be an increase of the moment of inertia because $I=\frac{2}{5}MR^2$. Thus, the angular speed $\omega$ would decrease and consequently the length of the day would increase.
