The initial phase difference between the particles is π/6. Option C
The farthest distance between two particles in SHM happens when they are the same distance from their starting points but going in different directions. This occurs when their movements have the same size but go in opposite directions.
(A) π/3: This means there is a phase difference of 120 degrees. The particles are not far enough apart and are not moving in opposite directions. Their movements wouldn't be the same distance.
(B) π/2: This means there is a difference of 90 degrees, which is too big. In this situation, the particles would be at their farthest points, not evenly spaced from their average positions.
(C) π/6: This means there's a difference of 30 degrees. This is the right answer. At this point, the particles are moving the same distance but in opposite directions, making the maximum distance a - 2.
(D) Zero: This means the particles are all lined up and moving together, so they won't spread out to the farthest distance.
Hence, the initial phase difference between the particles is π/6.