First Process: When a person push the wall, then the wall is displaced from one point to another. The person is pushing the wall which means he is applying the external force to the wall but the wall is not displacing. As the wall does not displaced therefore, the distance covered by the wall is zero.
Now, the work done is given as the product of force applied to the object with the distance covered. Since the distance covered is zero therefore, work done is also zero.
Second Process: When a person holds some luggage on the head, then the work done is said to be zero. Because the force acting on the person is in perpendicular direction and the work done also depends upon the cosine angle between force acting and the distance covered. As the distance is covered along horizontal direction and the force is applied in the vertical direction therefore, angle between them is 90 degree and cosine of 90 degree is zero.
Therefore, the work done by the person carrying the luggage is zero.
