The rod would be like a piece of spaghetti.
You’d basically start to reel in the rod around you, much like winding a wire into a spool, just it would take a lot more effort. At first it would feel like the rod was rigidly tied off, and it is – anchored to millions of tons of rod behind it. After pulling for some time the length of the rod under tension would start to be many miles long as the pull propagates down the rod at the speed of sound in its material, this would appear to give your some slack, because you’re basically stretching mile upon mile of the rod, so would get noticeable elongation at your end and the appearance of having freed up the attached end somewhat.
The other end of the rod wouldn’t feel anything until many years later as the first movement finally propagated to the end at the speed of sound in the rod material.
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