A body of mass m is slowly transported in the earth’s uniform gravitational field from point A(0,0) to point B(L,0) along the x–axis and then from B to point C(L,H) along the y–axis. The downward direction is taken as negative y-axis.
(i) Derive an expression for the work done by gravity during the motion along the two-segment path A→B→C.
(ii) The same body is now taken directly from A(0,0) to D(0,H) along the y-axis. Calculate the work done by gravity for this single-segment motion.
(iii) Compare your answers to (i) and (ii). State clearly what conclusion can be drawn about the nature of the gravitational force from this comparison.