Wheels and revolutions A car moves at 47.52 km/h. Its wheel radius is 21 cm. Approximately how many revolutions per minute does the wheel make?

Difficulty: Medium

Correct Answer: 600 rpm

Explanation:


Introduction / Context:
Revolutions per minute (rpm) equals the linear distance traveled per minute divided by the wheel circumference. Convert speed units to meters per minute; compute circumference from radius.



Given Data / Assumptions:

  • Speed = 47.52 km/h.
  • Radius r = 21 cm = 0.21 m.
  • Use circumference C = 2 * pi * r; with pi ≈ 22/7 for neat arithmetic.


Concept / Approach:
rpm = (linear speed in m/min) / C.



Step-by-Step Solution:

Linear speed = 47.52 * 1000 / 60 = 792 m/minCircumference ≈ 2 * (22/7) * 0.21 = 1.32 mrpm ≈ 792 / 1.32 = 600


Verification / Alternative check:
Using pi ≈ 3.1416 gives C ≈ 1.319, rpm ≈ 600.2, still rounds to 600 rpm.



Why Other Options Are Wrong:
200, 250, 300 are far too small given the circumference and speed.



Common Pitfalls:
Forgetting to convert km/h to m/min or using diameter instead of radius in the circumference formula.



Final Answer:
600 rpm

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