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Poisson’s ratio of a material is 0.5 percentage change in its length is 0.04% what is change in percentage of diameter (a) 0.02% (b) 0.03% (c) 0.4% (d) 0.05%

Poisson’s ratio of a material is 0.5 percentage change in its length is 0.04% what is change in percentage of diameter
(a) 0.02% (b) 0.03%
(c) 0.4% (d) 0.05%

Grade:Upto college level

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
3 years ago
Dear student

The answer is option a

Regards
Vikas TU
14149 Points
3 years ago
Note: I am writing sigma as ⊂.
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.
 
 

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