Rope Around The Earth Add 1 Meter

This puzzle is somewhat counter intuitive. Now let us tie a rope tightly around its equator. 15cm that s how far off the ground we re lifting the string remember out of 6 370km is close to one part in forty million.

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Suppose We Pulled A Rope Tight Around A Great Circle Around The Earth For Example Around The Equator Then We Make The Rope One Meter Longer How High Can We Pull The

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You add an extra 3 feet to the length.

Rope around the earth add 1 meter.

If you have reasoned the answer and can t believe it you are probably right. Rope around the world you have a piece of rope that just fits around the earth. Then imagine placing this longer rope back around the earth s equator. Now imagine lifting off this very long rope don t ask me how cutting it somewhere so as to stitch into it exactly one meter of extra rope.

All around the earth the rope is raised up uniformly as high as is possible to make it tight again. In a common version of this puzzle string is wrapped around the equator of a perfectly spherical earth. Imagine a rope tied around the earth s equator like a ring on a person s finger. The radius of earth is 6371 km approx.

Now imagine the rope is made just one meter longer and lifted uniformly off the surface until it is once again taught. Suppose you tie a rope tightly around the earth s equator. What will its height be above the surface. From the diagram it s pretty clear it s one foot.

The string is now rearranged so that it is at a uniform height above the equator. This string is cut and a piece 1 metre 3 ft 3 in in length is added in. Now untie the rope and add an extra 1 meter of rope and make it a perfect circle and place it around the. In fact this brain teaser requires neither an exact measurement of the earth s circumference which in fact varies by many kilometers depending on which circumference you measure nor even an assumption that the earth has a circular cross sect.

From there it s not hard to believe that adding 3 feet to a rope around the actual earth would raise it almost 6 inches. If you put 1 metre high sticks right around the equator and lay the rope on top how much longer does the rope need to be to make ends meet. How high is that. Divide again by pi to get the earth s radius 6 370km.

Imagine a rope that fits snugly all the way around the earth like a ring on a person s finger. The idea is to imagine the earth is a cube or just a square really and ask yourself if you added say 8 feet to the rope how far would that raise it above the square earth.

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