Question: 23: A gravitational field is present in a region and a mass is shifted from A to B through different paths as shown. If \mathrm{W}_{1}, \mathrm{~W}_{2} and \mathrm{W}_{3} represent the work done by the gravitational force along the respective paths, then :
(1) \mathrm{W}_{1}=\mathrm{W}_{2}=\mathrm{W}_{3}
(2) \mathrm{W}_{1}>\mathrm{W}_{2}>\mathrm{W}_{3}
(3) \mathrm{W}_{1}>\mathrm{W}_{3}>\mathrm{W}_{2}
(4) \mathrm{W}_{1}<\mathrm{W}_{2}<\mathrm{W}_{3}
Answer: Option (1)
Explanation:
Gravitational force is a conservative force. For a conservative force, the work done depends only on the initial and final positions, not on the path taken.
In this case, the mass moves from point A to point B along three different paths.
Since gravitational force is conservative, the work done along all paths is the same.
Thus, \mathrm{W}_{1} = \mathrm{W}_{2} = \mathrm{W}_{3}.
Therefore, the correct option is (1).