A) 3%
B) 2.5%
C) 1%
D) 0.5%
Correct Answer: B
Solution :
[b]: Poisson?s ratio, \[\sigma =\frac{\Delta d/d}{\Delta l/l}\] Area, \[A=\pi {{r}^{2}}=\pi \frac{{{d}^{2}}}{4}\] \[(\because d=2r)\] \[\therefore \]\[\Delta A=\frac{2\pi d\Delta d}{4}=\frac{\pi }{2}d\Delta d\] \[\therefore \]\[\frac{\Delta A}{A}=\frac{\pi \frac{d}{2}\Delta d}{\pi \frac{{{d}^{2}}}{4}}=2\frac{\Delta d}{d}\] Given: \[\frac{\Delta A}{A}\times 100=2%\] \[\therefore \]\[2=2\frac{\Delta d}{d}\times 100\,\text{or}\frac{\Delta d}{d}\times 100=1%\] ?(i) Given:\[\sigma =\frac{\Delta d/d}{\Delta l/l}0.4\,\text{or}\,\frac{\Delta d}{d}=0.4\frac{\Delta l}{l}\] \[\therefore \]\[\frac{\Delta l}{l}\times 100=\frac{1}{0.4}\,\frac{\Delta d}{d}\times 100\] \[=2.5\times 1%\text{ }=2.5%\] (Using (i))
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