Three blocks, each of same mass m, are connected with wires W₁ and W₂ of same cross-sectional area a and Young’s modulus Y. Neglecting friction the strain developed in wire W₂ is

 

If the system moves with acceleration a and T is the tension in the string W₂ then by comparing this condition from standard case

$\Rightarrow T=\frac{m_1{m}_2}{m_1+m_2}g$

In the given problem $m_1=(m+m)=2m and m_2$.

$$\begin{gathered} \therefore Tension =\frac{m.2m.g}{m+2m}=\frac{2}{3}mg \\ \therefore Stess =\frac{T}{a}=\frac{2}{3a}mg and \\ Strain = \frac{Stress}{Young\text{'}s modulus}=\frac{2}{3}\frac{mg}{aY} \end{gathered}$$