Explanation:

The work done by a force is defined as the product of the magnitude of the force and the displacement of the object in the direction of the force. In the case of a centripetal force, the force is always directed towards the center of the circle and is perpendicular to the displacement of the object. Therefore, the work done by a centripetal force is always zero.

Let's break down the explanation:

**Centripetal Force:**
A centripetal force is the force that keeps an object moving in a circular path. It is always directed towards the center of the circle and acts perpendicular to the motion of the object. Examples of centripetal forces include tension in a string, gravitational force, and electromagnetic force.

**Work Done by a Force:**
Work is defined as the product of the magnitude of the force and the displacement of the object in the direction of the force. Mathematically, work (W) is given by the equation W = F * d * cos(theta), where F is the magnitude of the force, d is the displacement, and theta is the angle between the force and displacement vectors.

**Centripetal Force and Displacement:**
In the case of a centripetal force, the force is always directed towards the center of the circle and acts perpendicular to the displacement of the object. This means that the angle theta between the force and displacement vectors is 90 degrees.

**Work Done by a Centripetal Force:**
When theta is 90 degrees, the cosine of theta is zero. Therefore, the work done by a centripetal force is given by W = F * d * cos(theta) = F * d * 0 = 0.

**Implications:**
From the above explanation, we can conclude that the work done by a centripetal force is always zero. It does not depend on the radius of the circle or the mass of the object. As long as the force is acting perpendicular to the displacement, no work is done.