The radii and Young's moduli of two uniform wires A and B are in the ratio 2 : 1 and 1 : 2 respectively. Both wires are subjected to the same longitudinal force. If the increase in the length of

Question

The radii and Young's moduli of two uniform wires A and B are in the ratio 2 : 1 and 1 : 2 respectively. Both wires are subjected to the same longitudinal force. If the increase in the length of the wire A is one per cent, the percentage increase in the length of the wire B is

TestHub · Accepted Answer

Increase in length l = FL AY or l = FL π r 2 Y Percent increase in length ∆ x = l L × 100 = F πr 2 Y Here, same longitudinal force is applied. So, ∆ x 1 ∆ x 2 = r 2 r 1 2 ⋅ Y 2 Y 1 1 ∆ x 2 = 1 2 2 ⋅ 2 1 = 1 4 × 2 1 1 ∆ x 2 = 1 2 ∆ x 2 = 1 × 2 = 2 %

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