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The poisson’s ratio of a material is 0.5. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by 4%. The percentage increase in the length is : (A) 1 % (B) 2% (C) 2.5% (D) 4%

aniket anand , 11 Years ago
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anser 2 Answers
Arun
Poisson's ratio =0.5
Since, density is constant therefore change in volume is zero, we have
V=A×l=constant
logV=logA+logl
or AdA+ldl=0
ldl=AdA
 Percentage increase in length = 4%
Last Activity: 5 Years ago
Vikas TU
Given Poisson's ratio (⊂) = 0.5.
Here, density is constant and hence change in volume is 0.
Given that there is a decrease in cross-sectional area by 4%
So, (dA/A) = 4.
We know that dA/A = 2 * (dr/r).
= > 4 = 2 * (dr/r)
= > 2 = (dr/r).

Hence,
= > dl/l
= > (dr/r)/⊂
= > 2/0.5
= > 4.

Therefore, the % increase in length = 4% (or) 0.04.
 
Last Activity: 5 Years ago
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