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Q.

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 length of the wire A is one percent, the percentage increase in length of the wire B is

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a

1.0

b

1.5

c

2.0

d

3.0

answer is .

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Detailed Solution

Young's modulus, Y = FLπr2∆Lor           ∆LL = Fπr2YFor the same force,          ∆LBLB∆LALA = (rArB)2(YAYB)            ∆LBLB = 2∆LALA             ∆LBLB×100 = 2(∆LALA×100) = 2%
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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 length of the wire A is one percent, the percentage increase in length of the wire B is