worn tire · Physics Brawl 2022 #6

Physics · mechanics

Problem

The tires on our new car have a diameter of D=634.5D = 634.5 mm and a tread depth of d0=8.0d_0 = 8.0 mm. The technician set the car's speedometer to measure accurately for this original wheel size. However, we drive frequently, so after a while, the tire tread came down to the minimum depth for summer use, dmin=1.6d_{\text{min}} = 1.6 mm. How does the actual speed now differ from the speedometer reading? Give the answer as the ratio of the speed on the speedometer to the actual speed.

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