A steel ball is rolling on smooth horizontal ice. Let us assume that there is no resistance to the movement of the ball

A steel ball is rolling on smooth horizontal ice. Let us assume that there is no resistance to the movement of the ball (friction against ice, air resistance). Is there any work being done?

Mechanical work A is determined by the formula: A = F * S * cosα. Where F is the force that acts on the body, S is the displacement of the body under the action of the force F, ∠α is the angle between the force F and the displacement S.
On a ball that rolls horizontally, only one force acts – the force of gravity m * g, directed vertically downward. The angle ∠α between the force of gravity m * g and the displacement of the ball S is 90, cos90 = 0.
If one of the factors is zero, then the whole product is equal to 0, A = 0.
Answer: the ball does not perform mechanical work A = 0.