Question

A particle moves on a circular path of radius 1 m. Find its displacement when it moves from \( A \rightarrow B \rightarrow A \). Also, its distance are it moves from \( A \rightarrow B \rightarrow A \).

• A. Distance = 2 m, Displacement = \( 4\pi \) m
• B. Distance = 2 m, Displacement = \( 5\pi \) m
• C. Distance = \( 4\pi \) m, Displacement = 2 m
• D. Distance = 2 m, Displacement = 2 m

Hint:

When a particle moves along a circular path and returns to its starting point, the distance is the length of the arc while the displacement is the straight-line distance between the two points.

Answer 1

The Correct Option is D

- The particle traverses a circular path of radius \( r = 1 \, \text{m} \). - The total path length from \( A \) to \( B \) and back to \( A \) is calculated. This involves covering half the circle in each direction. The total distance is the perimeter of the semicircle: \[ \text{Distance} = \pi r = \pi \times 1 = \pi \, \text{m}. \] - Displacement is defined as the shortest straight-line distance between the initial and final positions. Since the particle moves from \( A \) to \( B \) and then directly back to \( A \) across the circle's diameter, the displacement is \( 2 \, \text{m} \). Therefore, option (4) is correct, stating a distance of \( 2 \, \text{m} \) and a displacement of \( 2 \, \text{m} \).