I'm running into what I believe to be a physical paradox in what I believe to be a poorly stated physics problem.

https://brilliant.org/weekly-problems/2018-11-26/basic/?p=3

If you can't get to the problem from the link:

"Charlie hangs a string horizontally between two walls and uses an identical string to hang weights vertically (in the center between the walls).

As he adds weights, the tensions in both strings increase.

Which string will break first?

Firstly, it shouldn't ignore elastic theory, but that's not necessarily the issue I want to discuss ( unless it resolves the issue).

Once a weight is hung the tensile force in the rope strung between the walls will be given by:

F = m*g/(2*sin( δ ))

where;

F = Tensile Force

m = mass of hung weight

δ = the angle between horizontal and the Tensile Force

g = acceleration due to gravity

I guess I'm disturbed by the apparent conclusion that the lighter the hanging mass, the lesser the angle δ, and F goes to infinity.

Is there some hidden limit taking interpretation that tames the infinity I'm missing, Is it an artifact of the deflection assumption, or am I completely wrong, and everything is consistent and well?

https://brilliant.org/weekly-problems/2018-11-26/basic/?p=3

If you can't get to the problem from the link:

"Charlie hangs a string horizontally between two walls and uses an identical string to hang weights vertically (in the center between the walls).

As he adds weights, the tensions in both strings increase.

Which string will break first?

Firstly, it shouldn't ignore elastic theory, but that's not necessarily the issue I want to discuss ( unless it resolves the issue).

Once a weight is hung the tensile force in the rope strung between the walls will be given by:

F = m*g/(2*sin( δ ))

where;

F = Tensile Force

m = mass of hung weight

δ = the angle between horizontal and the Tensile Force

g = acceleration due to gravity

I guess I'm disturbed by the apparent conclusion that the lighter the hanging mass, the lesser the angle δ, and F goes to infinity.

Is there some hidden limit taking interpretation that tames the infinity I'm missing, Is it an artifact of the deflection assumption, or am I completely wrong, and everything is consistent and well?