To solve this problem, let's first understand what is being asked. The question concerns an object undergoing uniform circular motion and the work done by the centripetal force over one complete circle.

In uniform circular motion, the object moves in a circle with a constant speed, although its velocity vector changes direction at every point along the path. The force that keeps the object moving in a circular path is the centripetal force, which always acts towards the center of the circle.

The key concept to address this question is the work done by a force. The formula for work done when a force \(F\) displaces an object through distance \(d\) at an angle \(\theta\) to the force is:

\(W = F \cdot d \cdot \cos\theta\)

For uniform circular motion:

• The direction of the centripetal force is always perpendicular to the direction of the displacement at any instant of time.
• This means the angle \(\theta\) between the force and the displacement is \(90^\circ\).

Since \(\cos 90^\circ = 0\), the work done \(W\) by the centripetal force is:

\(W = F \cdot d \cdot \cos 90^\circ = 0\)

Thus, the work done by the centripetal force over a full circle is zero.

Let us analyze the given options:

• \((MV^2/r) \cdot 2r\) - Incorrect, since it assumes non-zero work.
• \(\text{Zero}\) - Correct, for the reasons explained above.
• \((Mv^2/r) \cdot 2\pi r\) - Incorrect, misapplies force-displacement relation; ensures incorrect understanding of force vector.
• \((MV^2/r) \cdot 2\pi r\) - Incorrect, similarly incorrect as it assumes non-zero work.

Therefore, the correct answer is 'Zero'.