Another Great Take Home Problem

Suppose I were to have an incredibly long piece of string, so long infact that I could wrap it tightly around the Earth.  Such a string would need to be, assuming the Earth has a radius of 4000 miles (sorry this is in miles…god I wish I could think in kilometers), 25132.7 miles long.  Now suppose I were to add just one inch to the string.  This would presumably give the string a little bit of slack.  The question is, how much slack?  If I were to grip the string and pull up on it perpendicular to the Earth, how far could I lift the string?  Far enough to just fit my hand under it?  To crawl under it?  To drive a bike under it?  To ride an elephant under it?

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