A gymnast of mass \(m\) with center of mass located a distance \(R\) from a horizontal bar swings upward along a vertical circular path about the bar. Two students evaluate the magnitude of the work done by gravity on the gymnast during two adjacent, equal angular intervals: Segment 1 (from \(\theta = 0^\circ\) at the lowest point to \(\theta = 45^\circ\)) and Segment 2 (from \(\theta = 45^\circ\) to \(\theta = 90^\circ\) at the horizontal position). Student 1 claims that the magnitude of the work done by gravity is greater during Segment 2 than during Segment 1. Student 2 claims that the magnitude of the work done by gravity is equal in both segments because the angular displacement \(\Delta\theta = 45^\circ\) is equal. Which student is correct, and why?