A body of mass ' m ' is moving slowly up the rough hill from point A to point B as shown in figure by a force which is acting tangential to surface at each point on the hill. Work done by this force is :

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The work done by the applied force is the sum of the work done against gravity and friction. The work against gravity is $m g h$ , dependent only on the height difference $h$ between A and B.

Since the applied force is always tangential and the motion is slow, the net force is approximately zero. Therefore, the total work done is independent of the specific shape of the trajectory, as the tangential force compensates for both gravity and friction along the path.

The work depends on the height difference and the path's roughness, but not its shape.

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