Consider two wires, A and B , composed of the same material. Wire A possesses a length l and diameter r , whereas wire B has a length 2l and diameter r/2 . When both wires are stretched by an identical force, the ratio

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Correct answer: D. 1/8

Young's modulus is given by Y = (F L)/(A Δ L) The elongation of a wire is Δ L = (F L)/(A Y) = (4 F L)/(π d^2 Y) For wire A , length L_A = l and diameter d_A = r . The elongation is: Δ L_A = (4 F l)/(π r^2 Y) For wire B , length L_B = 2l and diameter d_B = r/2 . The elongation is: Δ L_B = (4 F (2l))/(π (r/2)^2 Y) = (32 F l)/(π r^2 Y) Taking the ratio of the elongations: (Δ L_A)/(Δ L_B) = ((4 F l)/(π r^2 Y))/((32 F l)/(π r^2 Y)) = (4)/(32) = (1)/(8)

Consider two wires, A and B , composed of the same material. Wire A...

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