Properties Of Solids And Liquids Question 301
Question: The density $ \rho $ 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{Beta }{{\rho _{0}}hgy} \right] $
D) $ \rho ={\rho _{0}}\left[ 1-\frac{B}{{\rho _{0}}gy} \right] $
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Answer:
Correct Answer: B
Solution:
Bulk modulus, $ B=-V _{0}\frac{\Delta p}{\Delta V}\Rightarrow \Delta V=-V _{0}\frac{\Delta p}{B} $
therefore $ V=V _{0}\left[ 1-\frac{\Delta p}{B} \right] $
Density, $ \rho ={\rho _{0}}{{\left[ 1-\frac{\Delta p}{B} \right]}^{-1}}={\rho _{0}}\left[ 1+\frac{\Delta p}{B} \right] $
where, $ \Delta p=p-p _{0}=h{\rho _{0}}g $
= pressure difference between depth and surface of ocean $ \rho ={\rho _{0}}\left[ 1+\frac{{\rho _{0}}gy}{B} \right] $ (As h = y)
