Question

why is the work done on an object moving with uniform circular motion zero ​

Answer 1

Work done is equal to Force acting in the direction of DISPLACEMENT times the displacement i.e. W=F.S where (.) is dot product.

What happens in circular motion is the force acting on a body moving in a circular track/path is always towards the centre but the direction of velocity is always tangential to the circular path at each and every point i.e. the direction of velocity is always in the direction of the tangent drawn at that point on the circular track and we know that velocity and displacement can't have different direction both must have to have the same direction, so this means that displacement is also in the direction tangential to the circular track. For work to be done we need component of force along the direction of displacement but displacement and force are at 90° at each and every point on the circular track and therefore the component of force along the direction of displacement will always be zero in case of a body moving in a circular track or a body performing circular motion , we know W=F.S or F.Scos(theta), since body is moving in circular track Fcos(theta)=0 , and hence whole term will be 0 i.e. Work done will be 0.

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Answer 2

Explanation:

For an object moving in uniform circular motion, the only force is the centripetal force, which points in a direction along the radius of the circle, and since the radius of the circle never changes, there is no displacement along this direction, and the work done by this force is zero.