Fluid Mechanics Viscosity Question 270
Question: The density p of water of bulk modulus B at a depth y in the ocean is related to the density at surface$ {\rho_{0}} $ by the relation
Options:
A) $ \rho ={\rho_{0}}\left[ 1-\frac{{\rho_{0}}gy}{B} \right] $
B) $ \rho ={\rho_{0}}\left[ 1+\frac{{\rho_{0}}gy}{B} \right] $
C) $ \rho ={\rho_{0}}\left[ 1+\frac{B}{{\rho_{0}}hgy} \right] $
D) $ \rho ={\rho_{0}}\left[ 1-\frac{B}{{\rho_{0}}hgy} \right] $
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Answer:
Correct Answer: B
Solution:
[b] Bulk modulus, $ B=-V_{0}\frac{\Delta p}{\Delta V}\Rightarrow \Delta V=-V_{0}\frac{\Delta p}{B} $ $ \Rightarrow ,V=V_{0}\left[ 1-\frac{\Delta p}{B} \right] $ $ \therefore ,Density,\rho ={\rho_{0}}{{\left[ 1-\frac{\Delta p}{B} \right]}^{-1}}={\rho_{0}}\left[ 1+\frac{\Delta p}{B} \right] $ where, $ \Delta \rho =\rho -{\rho_{0}}=h{\rho_{0}}g $ = pressure difference between depth and surface of ocean $ \therefore ,,\rho -{\rho_{0}}\left[ 1+\frac{{\rho_{0}}gy}{B} \right] $ (As h=y)
BETA
