NEET Class neet Answered
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, 16:13: PM
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](https://images.topperlearning.com/topper/tinymce/cache/ddfa7083502c57d44c68db5154777992.png)
![begin mathsize 14px style fraction numerator increment d over denominator d end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/ddfa7083502c57d44c68db5154777992.png)
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](https://images.topperlearning.com/topper/tinymce/cache/e4a7a0fb3179e84f7bdbb9def973f2b6.png)
![begin mathsize 14px style fraction numerator increment l over denominator l end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/e4a7a0fb3179e84f7bdbb9def973f2b6.png)
Then poisson's ratio is
. . . . . . . . . . . . . . . . (1)
![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](https://images.topperlearning.com/topper/tinymce/cache/8326f625fc380a05da0081dbec4cd69c.png)
If change in diameter is 2% , then
. . . . . . . . . . . . . . .(2)
![begin mathsize 14px style fraction numerator increment d over denominator d end fraction space equals space 0.02 end style](https://images.topperlearning.com/topper/tinymce/cache/720c449cdc872481de735644c90bf285.png)
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](https://images.topperlearning.com/topper/tinymce/cache/b1d725d62d6cc5d3be2bb447e5b163d1.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/b1d725d62d6cc5d3be2bb447e5b163d1.png)
Hence change in length is 5%
Answered by Thiyagarajan K | 10 Sep, 2023, 21:59: PM
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