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A uniform cylindrical wire is subjected to a longitudinal tensile stress of 5×107 Nm-2. The Young's modulus of the material of the wire is 2×1011 Nm-2. The volume change in the wire is 0.02%. The factional change in the radius is

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a

0.25×10-4

b

0.5×10-4

c

1.0×10-4

d

1.5 × 10-4

answer is A.

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Detailed Solution

Y = stress∆LL or ∆LL = stressY = 5×1072×1011 = 2.5×10-4Now, V = πr2L ∆VV = π∆(r2L)πr2Lor ∆VV = r2∆L+L×2r∆rr2Lor ∆VV = ∆LL+2∆rror 2∆rr = ∆VV-∆LLor 2∆rr = 0.02100-2.5×10-4or ∆rr= 1×10-4 -2.52×10-4 = -0.25×10-4

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