An athlete completes one round of a circular track of radius ‘R’ in 40 seconds. His displacement at the end of 2 minutes 20 seconds will be?

1. A

   2R

2. B

   Zero

3. C

   2πR

4. D

   4R

Appeared in: KPSC Staff Nurse - 2016

Explanation

• The total time of motion is 2 minutes 20 seconds, which is equal to 140 seconds.
• Given that one round takes 40 seconds, the athlete completes a total of 140 / 40 = 3.5 rounds.
• After 3 complete rounds, the athlete returns to the starting position. The final 0.5 round moves the athlete to the point diametrically opposite the start.
• Displacement is the shortest straight-line distance between the start and end points. For diametrically opposite points on a circle, this distance is the diameter.
• The diameter of a circle with radius 'R' is 2R.

Why Other Options Were Wrong

• Option B: Displacement is zero only when the final position is identical to the starting position.
• Option C: This value, 2πR, represents the circumference of the track. Circumference is the distance covered in one full round, not the displacement.
• Option D: This value is twice the diameter and does not correspond to the displacement after 3.5 rounds. It has no direct physical significance in this problem.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of displacement in uniform circular motion as background academic context rather than a clinical decision trigger.
• Understanding the distinction between scalar quantities (like distance, which has magnitude only) and vector quantities (like displacement, which has both magnitude and direction) is a fundamental concept in physics.
• This principle is not limited to circular motion and applies to any form of movement, including oscillations, projectile motion, and orbital mechanics.
• The concept of displacement is crucial for calculating velocity (displacement over time) versus speed (distance over time).

How to Approach the Question

• Step 1: Identify the key parameters given in the problem: radius (R), time for one revolution (40 s), and total time of motion (2 min 20 s).
• Step 2: Convert all time measurements to a single, consistent unit. Convert 2 minutes 20 seconds to seconds: (2 * 60) + 20 = 140 seconds.
• Step 3: Calculate the total number of revolutions completed by dividing the total time by the time per revolution: 140 s / 40 s = 3.5 revolutions.
• Step 4: Analyze the final position based on the number of revolutions. Whole numbers of revolutions (3) mean the object returns to its starting point. The fractional part (0.5) determines the final position relative to the start.
• Step 5: A 0.5 revolution means the final position is halfway around the circle, which is diametrically opposite the starting point.
• Step 6: Recall the definition of displacement: the shortest straight-line distance between the initial and final points. For two diametrically opposite points, this distance is the diameter of the circle (2R).

Concept Tested & Keywords

• Concept Tested: Calculation of displacement in uniform circular motion.
• Stem keywords: circular track, radius R, 40 seconds, 2 minutes 20 seconds, displacement
• Lead-in keywords: will be

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QAOnDrh6SVq-V1A5fkLGDP

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