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 1
 Homework Statement

A wire of unstretched length ##l_o## is extended by a distance ##10^{3}l_o## when a certain mass is hung from its bottom end. If this same wire is connected between two points, A and B, that are a distance ##l_o## apart on the same horizontal level, and the same mass is hung from the midpoint of the wire as shown, what is the depression y of the midpoint, and what is the tension of the wire?
https://imgur.com/niVACGg
 Homework Equations

Hook's Law:
##F=kx##
I would assume that all the tension in the wire originates from the weight of the mass, and is equal to ##T=mg##, but that is incorrect.
Forming a right triangle with a hypothenuse denoted by ##x## and applying Pythagoras theorem:
\begin{cases}x^2=y^2+l_o^2 \\ x+y=l_o+\Delta l\end{cases}
Solving for ##y## I get:
$$y=\frac{0.01l_o⋅ 2.01}{2.02}≈0.01l_o$$
which is too incorrect.
The answers given by my textbook:
##y=l_o/20##
##T=5mg##
How can I arrive at those?
Forming a right triangle with a hypothenuse denoted by ##x## and applying Pythagoras theorem:
\begin{cases}x^2=y^2+l_o^2 \\ x+y=l_o+\Delta l\end{cases}
Solving for ##y## I get:
$$y=\frac{0.01l_o⋅ 2.01}{2.02}≈0.01l_o$$
which is too incorrect.
The answers given by my textbook:
##y=l_o/20##
##T=5mg##
How can I arrive at those?