Ten Metres That Should Mean Nothing
There is a rope tied tightly around the equator. Someone cuts it, adds ten metres, joins it again and somehow distributes the extra length evenly around the whole Earth. The question is simple: how high above the ground does the rope rise?
The first answer that comes to mind is usually some version of “almost nowhere.” The Earth is roughly forty thousand kilometres around. Ten metres spread across that distance feels like dust. Maybe the rope lifts by a fraction of a millimetre. Maybe not even that. The scale of the Earth swallows the extra length before the mind has had time to calculate anything.
The calculation, unfortunately for intuition, is embarrassingly short. The circumference of a circle is \(C = 2\pi r\). If the circumference grows by ten metres, the radius grows by \(10 / 2\pi\), which is about 1.59 metres.
So the rope is not brushing the grass....
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