Question

Three blocks, each of same mass m, are connected with wires $W_1$ and $W_2$ of same cross- sectional area a and Young's modulus Y. Neglecting friction the strain developed in wire $W_2$ is

• A. $\frac{2}{3}\frac{mg}{aY}$
• B. $\frac{3}{2}\frac{mg}{aY}$
• C. $\frac{1}{3}\frac{mg}{aY}$
• D. $\frac{3mg}{aY}$

Answer 1

The correct option is A $\frac{2}{3}\frac{mg}{aY}$

If the system moves with acceleration a and T is the tension in the string $W_2$ then by comparing this condition from standard case $T=\frac{m_1{m}_2}{m_1+m_2}g$
In the given problem $m_1=(m+m)=2m$ and $m_2=m$
$\therefore$ Tension = $\frac{m.2m.g}{m+2m}=\frac{2}{3}mg$
$\therefore$ Stress = $\frac{T}{a}=\frac{2}{3a}mg$ and $Strain=\frac{\text{Stress}}{\text{Young's modulus}}$ = $\frac{2}{3}\frac{mg}{aY}$