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Work done by centripetal force is always zero whenever the objects moves in a circular path because the direction of force is always perpendicular to the direction of displacement. So the examples are a car moving in a circular track, a ball moving in a circular path tied to a string etc.

The work done by centripetal force acting on planets by sun is not always zero as the path is elliptical and a component of the centripetal force is along the displacement. So in this case, there is a non-zero work done by the centripetal force.
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Work done by centripetal force is zero when a body moves in a uniform motion along a circular path.  Here the radius is perpendicular to the tangent on the circle.  The centripetal force is along the radius and the velocity and displacement is along the arc &  tangent.  Hence their product is zero.

examples :  Whirling a stone after tying to a stone.  Movement of electron in an atom.  Work done by movement of a bob of pendulum tied to a sting or thin rod.

WOrk done by centripetal force is not always zero, if the body is moving in an ellipse or some other irregular curve then there is some work done as the radius of the curvature changes.  As radius of curvature changes, the product of  Δr and Force will not be zero.  If we go around in a curve on a curved road, the work done by centripetal force is not zero , if the path taken is not a circle.

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