The translation of the CG, which is at the geometric center for both spheres, is governed by ${\bf F} = m {\bf a}$, where ${\bf a}$ tracks the CG. You might say that since both spheres have the same mass, they will translate in the same way, but ${\bf F}$ becomes different for each sphere as time evolves.

If you attach a unit tangent vector ${\bf e}_t$ to the rim of the sphere, then ${\bf F}$ may be represented as ${\bf F} = F {\bf e}_t$. $F$ is the same for either sphere, but the evolution of ${\bf e}_t$ will depend on how quickly each sphere rotates. The sphere with the higher moment of inertia, for example, will rotate slower, and so ${\bf F}$ will spend more time initially vertical than in the case of the other sphere.

Therefore, the translation is different for each sphere.

The translation of the CG, which is at the geometric center for both spheres, is governed by ${\bf F} = m {\bf a}$, where ${\bf a}$ tracks the CG. You might say that since both spheres have the same mass, they will translate in the same way, but ${\bf F}$ becomes different for each sphere as time evolves.

If you attach a unit tangent vector ${\bf e}_t$ to the rim of the sphere, then ${\bf F}$ may be represented as ${\bf F} = F {\bf e}_t$. $F$ is the same for either sphere, but the evolution of ${\bf e}_t$ will depend on how quickly each sphere rotates. The sphere with the higher moment of inertia, for example, will rotate slower, and so ${\bf F}$ will spend more time initially vertical than in the case of the other sphere.

Therefore, the translation is different for each sphere.

Edit: Sorry I misunderstood the question. My answer is for the case where there is a follower force that is applied at the same material point for all time. The question was about a dead load applied to different material points in time.