The small gear has 10 teeth and the big gear has 50 teeth. When the small gear rolls around the big gear, how many times will the arrow return to its initial orientation (pointing upward)?

Correct answer: C. 6 times

A. 5 times
B. 10 times
C. 6 times
D. 8 times

Explanation

To determine how many times the arrow on the small gear returns to its initial orientation, consider two factors: the rotations from rolling along the equivalent distance of the big gear's circumference, and the additional rotation due to the gear's circular path.First, the small gear with 10 teeth rolls around the big gear with 50 teeth. If the small gear were rolling on a flat surface covering a distance equal to the big gear's circumference, it would rotate 5 times, as 50 (teeth of big gear) divided by 10 (teeth of small gear) equals 5. However, because the small gear is not only rolling but also rotating around the big gear, it makes one additional rotation due to the circular path it follows.Thus, the arrow returns to its initial orientation 5 + 1 = 6 times. The other options incorrectly account for the rotations by either ignoring the additional circular rotation (5 times) or adding unnecessary rotations (10 times and 8 times).

Last updated 3 September 2026

The small gear has 10 teeth and the big gear has 50 teeth. When the small gear rolls around the big gear, how many times will the arrow return to its initial orientation (pointing upward)?

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