Question

Why is the work done on an object moving with uniform motion zero?

Answer 1

As you have used the word uniform motion which says that the object is moving with a constant angular velocity. So the angular acceleration of the object is zero. This suggest that no external force is acting on the system and thus the work done is zero too.

Answer 2

work is said to be done by a force when the force produces a displacement in the body on which it acts in any direction except  perpendicular to the direction of the force. That's why the work done on an object moving with uniform motion .