A uniform sphere is situated on a smooth horizontal surface, and a...

For a sphere placed on a smooth horizontal surface, there is no frictional force acting between the sphere and the surface.

The only horizontal force acting on the sphere is the applied force $F$.

By Newton's second law of motion for the center of mass, the net external force is equal to the product of mass and the acceleration of the center of mass.

$F = Ma$

$a = \dfrac{F}{M}$

This expression shows that the linear acceleration $a$ of the center of the sphere depends only on the applied force $F$ and the mass $M$ of the sphere. It is completely independent of the height $h$ at which the force is applied.

The height $h$ determines the torque and thus the angular acceleration of the sphere, but it has no effect on the translational acceleration of the center of mass.