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Find the depth of lake at which density ...

Find the depth of lake at which density of water is `1%` greater than that at the surface. Given compressibility `k= 50 xx10^(-6) atm^(-1)`.

Text Solution

Verified by Experts

`B=(/_\p)/(-(/_\V)/V)implies (/_\V)/V+-(/_\p)/B`

We know `p=p_(atm)=hrhog`
or `m=rhoV=const`
`drhov+dvrho=0`
`drhoV+dVrho=0`
`implies(drho)/rho=-(dV)/V`
i.e., `(/_\rho)/rho=(/_\rho)/B`
`implies(/_\rho)/rho=1/100`
`1/100=(hrhog)/B` [assuming `rho=const.]`
`hrhogB/100=1/(100k)`
`hrhog=(1xx1xx10^(5))/(100xx50xx10^(-6))`
`h=(10^(5))/(5000xx10^(-6)xx1000xx10)=(100xx10^(3))/50=2km`
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