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(B) The extension $l$ in a rod is given by the formula $l = \frac{FL}{AY} = \frac{FL}{\pi r^2 Y}$,where $F$ is the force,$L$ is the length,$A$ is the

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$L = 100 \ cm, D = 2 \ mm$

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(B) The extension $l$ in a rod is given by the formula $l = \frac{FL}{AY} = \frac{FL}{\pi r^2 Y}$,where $F$ is the force,$L$ is the length,$A$ is the cross-sectional area,$r$ is the radius,and $Y$ is Young's modulus.Since the rods are identical ($Y$ is constant) and the force $F$ is the same,the extension $l$ is proportional to $\frac{L}{r^2}$ or $\frac{L}{D^2}$ (where $D$ is the diameter).Calculating the ratio $\frac{L}{D^2}$ for each option:$(a)$ $\frac{10}{1^2} = 10$$(b)$ $\frac{100}{2^2} = \frac{100}{4} = 25$$(c)$ $\frac{200}{3^2} = \frac{200}{9} \approx 22.22$$(d)$ $\frac{300}{4^2} = \frac{300}{16} = 18.75$Comparing these values,the ratio is maximum for option $(b)$.

Four identical rods are stretched by the same force. The maximum extension is produced in:

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