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Q.

A uniform cylindrical wire (Young’s modulus =2×1011N m−2 ) is subjected to a longitudinal tensile stress of 5×107N m−2 . If the overall volume change in the wire is 0.02%, the fractional decrease in the radius of the wire is

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a

1.5×10−4

b

1.0×10−4

c

1.5×10−4

d

0.5×10−4

answer is D.

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Detailed Solution

Strain=Δll=StressY=5×1072×1011= 2.5×10-4 V=πr2l∴ΔVV=2Δrr+Δll or Δrr=12ΔVV-Δll = 122×10-4 +2.5×10-4  =0.5×10-4
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A uniform cylindrical wire (Young’s modulus =2×1011N m−2 ) is subjected to a longitudinal tensile stress of 5×107N m−2 . If the overall volume change in the wire is 0.02%, the fractional decrease in the radius of the wire is