Binding Rope Around The Earth

Rope around The Earth:

Wrap a thread tightly around the earth (along the equator). Now add an extra 2 meters of thread to this length and then wrap the new thread again around the earth in the same circular path (i.e. along the equator).

(Image: Binding rope around the Earth)

Now, how high do you think will the thread rise above from the ground ?(Or in other words, what will be the new radius corresponding to this new circumference?)

Well, practically one might think that an addition of 2 meter won't make any difference since its too small compared to the size of the earth (which is ~6371000 meters in radius!).

And even if it does, the difference will be so small (may be in millimeters or so) that it can easily be neglected? Well, lets compute it. Let R be the initial radius of the loop in meters(which will be equal to radius of the earth since the thread was tightly wrapped along the equator around the earth).

Let R' be the new radius after an addition of 2 m in the total length.

So, (2*pi*R) + 2 = 2*pi*R' (where pi = 3.14)

=> R' - R = 1/(pi) = 0.318 meters ~ one-third of a meter !

Adding even a mere 2 meter of thread to such a huge length will cause the thread to get lifted by one-third of a meter along the entire surface of the earth!

#mathematics #mathskills #maths

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