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

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Solution

The correct option is A
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 $m_{1} = (m + m) = 2 m$ and $m_{2} = m$
$∴$ Tension = $\frac{m .2 m . g}{m + 2 m} = \frac{2}{3} m g$
$∴$ Stress = $\frac{T}{a} = \frac{2}{3 a} m g$ and $S t r a i n = \frac{Stress}{Young's modulus}$ = $\frac{2}{3} \frac{m g}{a Y}$

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