Question

Three wheels can complete 60, 36, and 24 revolutions per minute. There is a red spot on each wheel that touches the ground at time zero. After how much time will all these spots will simultaneously touch the ground again?

• A. \( \frac{5}{2} \, \text{s} \)
• B. \( \frac{5}{3} \, \text{s} \)
• C. 3.1 s
• D. Cannot be determined

Hint:

To find when multiple periodic events occur together, find the least common multiple (LCM) of the periods of the events.

Answer 1

The Correct Option is C

The time taken for one revolution is the inverse of the revolutions per minute. Therefore, the time for one revolution of each wheel is: - For the first wheel: \( \frac{1}{60} \) minute per revolution = \( \frac{1}{60} \times 60 = 1 \, \text{sec} \). - For the second wheel: \( \frac{1}{36} \) minute per revolution = \( \frac{1}{36} \times 60 = 1.66 \, \text{sec} \). - For the third wheel: \( \frac{1}{24} \) minute per revolution = \( \frac{1}{24} \times 60 = 2.5 \, \text{sec} \). The least common multiple of 1, 1.66, and 2.5 is 3.1 seconds. Therefore, all three spots will touch the ground again after 3.1 seconds.