Question

Why is the work done on a object moving with uniform circular motion zero

Answer 1

As you have used the word uniform motion which says that the object ismoving 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

workdone = force × displacement
when object moves in circular motion it makes a close loop..and net displacent is 0.
so,
workdone= force×0=0...

i think it will help you