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Ok, let's consider the situation where one end is attached to a wall.
Firstly, the 100 N weight loads a 100 N tension 'T' onto the chord.
Now the reaction 'R' on the wall is equal and oppositely directed - by Newton's 3rd Law. That is, the reaction 'R' of the wall on the chord is also 100 N.
So T = R = 100 N
If we replace the wall with a weight equal to 100 N we can see that there is ultimately no difference and that the reaction of the wall being 100 N is now just a weight of 100 N.
The scale will read 100 N
*Edit: I’ll see if I can clarify things.
If you’re still not sure that the wall pulls with a reaction force of 100 N in the opposite direction, consider if there were no force pulling in the opposite direction. There would be nothing holding the weight in place and the scale wouldn’t have anything to pull back on, there would be no tension for it to read and the weight would fall to the floor.
Once you’re convinced of that fact, that the wall pulls in the opposite direction with a reaction force of 100 N, then it’s easier to understand how replacing the wall with anything else that can provide that 100 N reaction force, such as another 100 N weight, will be equivalent to the wall and keep the system stationary.
@Steve Bukoan