A boy completes one round of a circular track of diameter 200 m in 30

A boy completes one round of a circular track of diameter 200 m in 30 s. What will be the displacement at the end of 3 minutes and 45 seconds ?

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50 m

100 m

200 m

236 m

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Answer is Wrong!

This question was previously asked in

UPSC CDS-1 – 2022

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The boy completes 7.5 rounds in 3 minutes and 45 seconds. After 7 complete rounds, the displacement is zero. The displacement after the remaining 0.5 rounds (half a round) is the straight-line distance between the starting point and the diametrically opposite point. This distance is equal to the diameter of the circular track.

Displacement is a vector quantity defined as the shortest straight-line distance between the initial and final positions. In circular motion, after completing one or more full rounds, the displacement is zero because the final position is the same as the initial position. After half a round, the final position is diametrically opposite the initial position.

The diameter of the track is 200 m, so the radius is 100 m. The time taken for one round is 30 s. Total time = 3 minutes 45 seconds = 180 + 45 = 225 s. Number of rounds = Total time / Time per round = 225 s / 30 s = 7.5. Displacement after 7.5 rounds is the same as displacement after 0.5 rounds. The starting point and the point diametrically opposite are separated by the diameter, which is 200 m.

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