A) - 4%
B) - 2%
C) - 1%
D) - 5%
Correct Answer: A
Solution :
[a] Given \[f=\frac{\rho }{2\ell }\sqrt{\frac{T}{\mu }}\] Taking log of both sides \[\log \,f=\log \left( \frac{p}{2} \right)-\log \ell +\frac{1}{2}\log T-\frac{1}{2}\log \mu \] Differentiating partially on both sides, \[\frac{df}{f}=0-\frac{d\ell }{\ell }+\frac{1}{2}\frac{dT}{T}-\frac{1}{2}\frac{d\mu }{\mu }\] or \[\frac{df}{f}\times 100=\left( -\frac{d\ell }{\ell }\times 100 \right)+\left( \frac{1}{2}\frac{dT}{T}\times 100 \right)-\left( \frac{1}{2}\frac{d\mu }{\mu }\times 100 \right)\]\[=(-1)+\frac{1}{2}(-2)-\frac{1}{2}(4)=-1-1-2=-4%\]You need to login to perform this action.
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