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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