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It would have to be about 6.3" longer:
Length of rope = 2 * Pi * radius
2*Pi*(r+1")-2*Pi*r=2*Pi*1" = ~6.3"
Let's say you have a loop of rope around the equater. How much longer would the rope need to be in order to have the rope lifted of off the ground by 1 inch all the way around the world?
Another way to pose this question would be . . . If the radius of the earth increased by 1 inch how much longer would the rope need to be?