What is the transverse diameter of a wheel that completes 113 rotations to traverse a distance of 2km 26 decameters?
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Answer: B. 6 4/11m
Explanation
Converting the total distance of 2 kilometers and 26 decameters gives 2260 meters of linear travel. Dividing the total distance by 113 rotations yields a wheel circumference of exactly 20 meters. Dividing the circumference by pi gives a transverse wheel diameter that simplifies to the mixed fraction 6 and 4/11 meters. Wheel rotation problems equate total linear travel distance to the wheel's circumference multiplied by the rotation count. The circumference of a circular wheel is calculated as pi multiplied by its transverse diameter. Unit conversions are required to harmonize metric units before performing circular distance calculations.
Automotive engineering and odometer design rely on wheel circumference calculations to measure vehicle speed and distance. Mechanical gear and pulley systems use rotational distance principles to synchronize moving parts. This applied physics problem combines metric conversion, circular geometry, and rotational kinematics. Option A underestimates the wheel diameter by miscalculating the circumference from the rotation count. Option C overestimates the wheel diameter, yielding a circumference too large for the given distance. Option D represents an incorrect fraction resulting from improper division of the circumference by pi.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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