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Physics Question 30 – JEE-MAIN 2025

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

The path 'ABAB' implies a sequence of movements: A to B, then B to A, then A to B.

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Ninja Strategy•Displacement Constraint Check

Recognize that displacement on a circular track cannot exceed the diameter (2r), immediately eliminating options with displacement greater than 2r. Then, determine the final position to find the exact displacement.

Step 1: Interpret the Path and Identify Start/End Points✦ Active

The sportsman traverses the path ABAB. This means the sequence of movement is A → B, then B → A, then A → B. The initial position is A, and the final position is B.

Step 2: Calculate Total Distance Traveled○ Expand

Each segment (A to B or B to A) along the circular track represents half a circumference. The circumference of the track is 2πr. Therefore, the distance for one segment is 12(2πr)=πr.

The total path ABAB consists of three such segments: (A → B) + (B → A) + (A → B).

Total Distance=πr+πr+πr=3πr
💡 Teacher's Secret Hint

Remember that distance is a scalar quantity and always adds up, regardless of direction.

Step 3: Calculate Total Displacement○ Expand

Displacement is the shortest straight-line distance from the initial position to the final position. The initial position is A and the final position is B.

Since A and B are diametrically opposite points on a circular track of radius r, the straight-line distance between them is the diameter.

Total Displacement=Diameter=2r

Thus, the distance travelled is 3πr and the displacement is 2r.

💡 Teacher's Secret Hint

Displacement is a vector quantity, so consider the net change in position from start to end.

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