Three metal balls are suspended by three wires (a, b & c) of equal length arranged in sequence as shown in figure. The masses of the balls, starting at the top are 2 kg, 4kg and 3 kg. The wire diameters in the same order are 2 mm, 1.2 mm & 1 mm respectively. What is the correct order of increasing stresses in the wires?

Correct option is A

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$$\begin{aligned}&\textbf{Calculate the Stress in Each Wire} \\&\text{Using } \sigma = \frac{F}{A}: \\[1em]&\text{1. Wire a:} \\&\sigma_a = \frac{9g}{\pi} \\[1em]&\text{2. Wire b:} \\&\sigma_b = \frac{7g}{0.36\pi} \approx \frac{19.44g}{\pi} \\[1em]&\text{3. Wire c:} \\&\sigma_c = \frac{3g}{0.25\pi} = \frac{12g}{\pi} \\[2em]&\textbf{Compare the Stresses} \\&\quad \sigma_a = \frac{9g}{\pi} \\&\quad \sigma_b \approx \frac{19.44g}{\pi} \\&\quad \sigma_c = \frac{12g}{\pi} \\[1em]&\text{The order of increasing stress is:} \\&\boxed{\sigma_a < \sigma_c < \sigma_b}\end{aligned}$$​​​