JEE Main 2025 · 2 April · evening · Single correct · +4 / −1
A sportsman runs around a circular track of radius r such that he traverses the path A B A B. The distance travelled and displacement, respectively, are
- (a) π r, 3 r
- (b) 2 r, 3 π r
- (c) 3 π r, 2 r
- (d) 3 π r, π r
Answer and solution
Answer (c) 3 π r, 2 r
Solution
Physics sir · 3 steps
Track the path in half-circles for distance, then look only at where he starts and where he stops.
- Count half-circles. A and B are at opposite ends of a diameter, so each leg A to B or B to A is half the circle, of length π r. The path ABAB has three legs: A to B, B to A, A to B.
distance = 3 × π r = 3π r
- Start and end. Displacement ignores the route taken. He starts at A and finishes at B, and the straight line joining them is a diameter, of length 2r.
- So. Distance is 3π r and displacement is 2r, which is option (c).
The idea to keep. Distance adds up every bit of path walked. Displacement is only the straight line from the start point to the end point, however winding the route.
Answer from the NTA final answer key. Solution by PrepWiser.