Final answer:
Correct option: (d) pushing on a plane horizontal surface
The work done is maximum when the force is applied in the direction of the displacement with no angle to reduce its effect. Thus, pushing on a plane horizontal surface results in the most work done, given that friction is negligible.
Step-by-step explanation:
The work done by a force on an object is given by the equation W = F × d × cos(θ), where W is the work, F is the force applied, d is the displacement of the object, and θ is the angle between the force and the displacement.
In the case described, the work done is maximum when the force is applied in the direction of the displacement. Therefore, the maximum work done will be when the boy is pushing the body over a smooth plane horizontal surface, as the force is parallel to the displacement and there is no angle (θ = 0 degrees, so cos(θ) = 1).
For the inclined plane, vertical lift, and smooth rollers, the force is not entirely in the direction of displacement, or there are other forces involved such as gravity, making the work done less than the maximum possible value.
It's important to note that while lifting a body vertically or pushing it up an inclined plane involves work against gravity, pushing on a horizontal surface typically involves less resistance and therefore can lead to greater work done if friction is negligible.