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2 persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. A 30 kg weight is attached to the rope at the mid-point which now no longer remains horizontal. What is the minimum tension required to completely straighten the rope?

What I got as the solution is that the tension would not be defined or let's say it would be infinite. Well this answer seems reasonable to me. What it actually means is that practically the rope will never straighten. It will be bent by some amount, however small, until there is some weight. But, my friends say that my answer is absurd, as one can see by experimenting that the rope will straighten. But I say that it's actually not happening. When we do experiments with normal rope and small weights, and apply the tension which seems to straighten the rope, the deformation is so small that naked eye cannot observe it. I have calculated this mathematically. But still my friends refuse to accept the answer.

So, I need a little help with this. If I'm really wrong, can somebody let me know what's the mistake?