An athlete completes one round of a circular track of diameter 100 m in 20 s. What will be the displacements after 1 minute and 10 s, respectively ?
0 m, 50 m
300 m, 100 m
300 m, 50 m
0 m, 100 m
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CDS-2 – 2021
After 1 minute (60 seconds), the athlete has completed 60 s / 20 s/round = 3 full rounds. In circular motion, after completing a full circle or multiple full circles, the displacement is zero because the final position is the same as the starting position. So, displacement after 1 minute is 0 m.
After 1 minute and 10 seconds (70 seconds), the athlete has completed 70 s / 20 s/round = 3.5 rounds. This is 3 full rounds plus half a round. After 3 full rounds, the displacement is zero. The remaining half-round takes the athlete from the starting point to the diametrically opposite point on the track. The displacement in this case is the straight-line distance between the starting point and the diametrically opposite point, which is equal to the diameter of the circle. The diameter is given as 100 m. So, displacement after 1 minute and 10 seconds is 100 m.
– For motion along a closed loop (like a full circle), the displacement is zero if the motion starts and ends at the same point.
– For motion along half a circle, the displacement is equal to the diameter.