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the poission's ratio of a material is0.4 if a force is applied to a wire of this material there is a decrease in the cross section area by 2%in such case the percentage increase in its length will be..?
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Asked by safasamreen103 | 10 Sep, 2023, 04:13: PM
answered-by-expert Expert Answer
Poisson's ratio ν  is the ratio of  transverse strain to lateral strain.
 
If a wire is pulled along the direction of length , then ratio of change in diameter Δd to its original diameter d is transverse strain.
 
Transverse strain = begin mathsize 14px style fraction numerator increment d over denominator d end fraction end style
 
If a wire is pulled along the direction of length , then ratio of change in length  to its original length is longitudinal strain.
 
Longitudinal strain = begin mathsize 14px style fraction numerator increment l over denominator l end fraction end style
 
Then poisson's  ratio is begin mathsize 14px style nu space equals space fraction numerator begin display style bevelled fraction numerator increment d over denominator d end fraction end style over denominator begin display style bevelled fraction numerator increment l over denominator l end fraction end style end fraction space equals space 0.4 end style . . . . . . . . . . . . . . . . (1)
If change in diameter is 2% , then begin mathsize 14px style fraction numerator increment d over denominator d end fraction space equals space 0.02 end style . . . . . . . . . . . . . . .(2)
Hence begin mathsize 14px style fraction numerator increment l over denominator l end fraction space equals space fraction numerator begin display style bevelled fraction numerator increment d over denominator d end fraction end style over denominator nu end fraction space equals space fraction numerator 0.02 over denominator 0.4 space end fraction space equals 0.05 space end style
Hence change in length is 5%
Answered by Thiyagarajan K | 10 Sep, 2023, 09:59: PM
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