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 moves along a circular path with radius \( r = 1 \, \text{m} \). - The distance from \( A \rightarrow B \rightarrow A \) is the length of the path covered. Since the particle covers half the circle when it moves from \( A \) to \( B \) and back from \( B \) to \( A \), the total distance covered is the perimeter of the semicircle: \[ \text{Distance} = \pi r = \pi \times 1 = \pi \, \text{m}. \] - The displacement is the shortest straight-line distance between the starting and ending points, which in this case is 2 meters, as it moves from \( A \) to \( B \) and back to \( A \), directly across the circle's diameter. Hence, the displacement is \( 2 \, \text{m} \). Thus, the correct option is (4), where the distance is \( 2 \, \text{m} \) and the displacement is also \( 2 \, \text{m} \).