Question

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

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

Answer 1

Answer: (A)

$\frac{2}{3}\frac{mg}{aY}$

Answer 2

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 $\mathbf{T =}\frac{\mathbf{m}_{\mathbf{1}}\mathbf{m}_{\mathbf{2}}}{\mathbf{m}_{\mathbf{1}}\mathbf{+}\mathbf{m}_{\mathbf{2}}}\mathbf{g}$

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

$\text{Strain} = \frac{\text{Stress}}{\text{Young's modulus}} = \frac{2}{3}\frac{mg}{aY}$