JEE Main & Advanced Sample Paper JEE Main Sample Paper-4

  • question_answer
    The poisson's ratio of a material is 0.4. If a force is applied to a bar of this material, there is a decrease of cross-sectional area by 2%. The percentage increase in its length is

    A)  3%                        

    B)  2.5 %   

    C)  1%                        

    D)  0.5%

    Correct Answer: B

    Solution :

    Position ratio as \[\sigma =\frac{\Delta d/d}{\Delta \ell /\ell }\And \frac{\Delta \ell }{\ell }=\frac{\Delta d/d}{\sigma }\] \[A=\pi {{r}^{2}}=\frac{\pi {{d}^{2}}}{4}\]or\[A=\log \left( \frac{\pi }{4} \right)+2\log d\] Differentiate the above equation \[\frac{\Delta A}{A}=\frac{2\Delta d}{d}\]or\[\frac{\Delta d}{d}=\frac{1}{2}\frac{\Delta A}{A}=\frac{1}{2}\times 2%=1%\] \[\frac{\Delta l}{l}=\frac{1%}{0.4}=2.5%\]

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