FILE No.196Unsolved
Assume the Earth is a perfect sphere and the length of the equator is about 40,000 km. A rope was wrapped tightly along this equator. The rope is lengthened by just 1 m and made to float at the same height all the way around above the ground.
About how large is the gap between the ground and the rope?
If you get stuck, open the hints one at a time, in order.
What is the relationship between circumference and radius?
Circumference = 2π × radius.
The radius increases by the increase in circumference divided by 2π.
About how large is the gap between the ground and the rope?
Choose the answer closest to the truth.
About 16 cm
The answer is "About 16 cm."
When the circumference increases by 1 m, the radius increases by 1 ÷ (2π) ≈ 0.16 m. This is the same regardless of the size of the Earth.
1 mm or 1 m come from confusing the increase in circumference with the radius.
Because the Earth is so big you think 1 m changes nothing.
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