Two wires A and B are made of same material. The wire A has a length l and diameter rwhile the wire B has a length 2l and diameter r/2. If the two wires are stretched by the same force, the elongation in A divided by the elongation in B is

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\text{ Let the Young's modulus of the wire's material be Y .} \text{ Here: } \text{ Force = F } A_1 = $\pi$ r^2 L_1 = l A_2 = $\pi$ \left( r/2 \right)^2 = $\pi$ r^$\frac{2}{4}$ \text{ L }_2 = 2\text{l } \text{ Let the elongation in A be x and that in B be y }. \text{ Since the Young's modulus for both the wires is the same: } Y = F/A_1/x/l = F/A_2/y/2l \Rightarrow x/y = A_2/2 A_1 \Rightarrow x/y = $\frac{1}{8}$

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