1.

The depth of a lake at which density of water is 2% greater than on surface. [Compressibility of water =50xx10^(-6)/atm , 1 atm = 10^5N//m^2]

Answer»

2 km
4 km
8 km
40 km

Solution :The variation of density with PRESSURE is given by `rho'=rho(1+(Deltap)/B)`
`because Deltap=hrhog` and `1/B=C` so r'=r(1+Ch`rho`g)
`rArr (rho'-rho)/rho=Chrhog`
`rArr H = (Deltarho)/rhoxx1/(Crhog)`
`=2/100xx1/((50xx10^(-6))/105 xx10^3xx10)`
`=2/5xx10^4 =20/5xx10^3`m = 4 km
OR
`rho=M/V rArr drho=-M/V^2 dV`
`rArr (drho)/rho=(-M/V^2dV)/(M/V)`
`rArr (drho)/rhoxx100% =-(dV)/Vxx100`
`rArr (dV)/V xx 100=2%[ "as" (drho)/rhoxx100%= 2%]`
Now `B=(DeltaP)/((DELTAV)/V)`
and compressibility `C=1/B` and `DeltaP=hrho g `
`1/C=(hrhog)/(2/100)`
`rArr h=2/100xx1/(V rhog) = 2/100xx1/((50xx10^(-6))/10^5 xx10^3xx10)m`
= 4 km


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