A small block of mass m is moved from point P(0,0) to point Q(R, R) in a vertical xy -plane (where the y -axis is vertical). The block is moved along three different paths as shown in the figure: Path 1: Along the circular arc PQ of radius R centered at O(0, R) . Path 2: Along the horizontal line PS to S(R, 0) and then vertically to Q . Path 3: Along the vertical line PO to O(0, R) and then horizontally to Q . If W₁,

Step-by-step solution

The gravitational force is a conservative force. The work done by a conservative force depends only on the initial and final positions of the particle and is independent of the path taken. Here, the initial point is P(0, 0) and the final point is Q(R, R) . The vertical displacement of the block is y = R - 0 = R . The work done by the gravitational force along any path between these two points is given by: W = -mg y = -mgR Since all three paths 1, 2, and 3 have the same initial and final points, the work done by gra