Question

please solve the question in the attachment below

Answer 1

This question is related to elasticity and Young's modulus Y.

Let L = Original length of wire when there is no tension (tensile force) .  A = area of cross section.  L1 and L2 are lengths of the wire when there are tensions (tensile stress) T1 and T2 acting on the wire along the length.  We assume that the area of cross section does not vary a lot when the wire is stretched.
     ΔL = extension of the wire when tensile stress is applied.

$Y=\frac{T/A}{\Delta L/L}=\frac{TL}{A \Delta L},\ \ Hence,\ AY\Delta L=TL\\\\AY(L_1-L)=T_1L_1\\AY(L_2-L)=T_2L_2\\\\Hence,\ (L_1-L)T_2L_2=(L_2-L)T_1L_1\\\\L(T_1L_1-T_2L_2)=L_1L_2(T_1-T_2)\\\\L=\frac{L_1L_2(T_1-T_2)}{T_1L_1-T_2L_2},\ \ \ \ ( T1 \neq T2 )$

This is  a simple expression.