Give an example of a situation in which there is a force and a displacement, but the force does no work. explain why it does no work

Work is equal to force times distance times cosine of the angle between the force and the path vector making it a scalar or dot product. Work is independent of the path taken. It refers to positive change in KE or negative change in PE.
 So for example if you lift a box from ground to waist height then, you did positive work over the distance you lifted it. If you pick it up to that same height, then put it back done on the ground at same place, then no work is done. 

Hope this makes sense. Any questions please ask. Thank You!

The circular motion of ball tied with a string is an example of having force and displacement and zero work done.

The displacement of the body due to application of force is known as work done on the body. The mathematical expression for the work done is given as,

Here, F is the magnitude of force, d is the displacement of the body and is the angle between the force and path vector.

From the above expression, it is clear that zero work done is possible for , which means that displacement vector (or path vector) should be perpendicular to the applied force.For example- A ball on a string spinning around in uniform circular motion. In this case, the centripetal force acting on the ball is perpendicular to its instantaneous velocity as well as instantaneous displacement. Therefore, the net work done on the ball by centripetal force is zero.

Thus, we conclude that the ball undergoing the circular motion through a string is an example of having force and displacement, but zero work done is obtained.

Learn more about the work done here:

link

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