Question

A sportsman runs around a circular track of radius $ r $ such that he traverses the path ABAB. The distance travelled and displacement, respectively, are:

• A. \( 2r, 3\pi r \)
• B. \( 3\pi r, \pi r \)
• C. \( \pi r, 3r \)
• D. \( 3\pi r, 2r \)

Hint:

When dealing with circular motion, remember that the displacement is the straight-line distance from start to end, and the distance is the total path length travelled.

Answer 1

The Correct Option is D

Displacement is the straight-line distance from the initial point to the final point. 
Since the sportsman runs around the circular track and ends up at the same position (A), the displacement is the straight-line distance through the circle’s center. Therefore: \[ \text{Displacement} = 2r \] The distance travelled is the total path length covered by the sportsman, which consists of two complete laps around the circular track. Thus, the total distance is: \[ \text{Distance} = 2\pi r + \pi r = 3\pi r \] Thus, the correct answer is: \[ 3\pi r, 2r \]