Please solve question 153?

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Answer 1 · 2018-04-07T07:19:36

The answer is #"option (2)"#

Let the atmospheric pressure be #a=10^5Pa#

Let the depth of the lake #=hm#

The density of water is #rho=10^3kgm^-3#

Then the pressure at half the depth of the lake is

#p_(1/2h)=a+rhogh/2=a+1/2rhogh#

The pressure at the bottom of the lake is

#p_(b)=a+rhogh/2=a+rhogh#

Then

#p_(1/2h)=2/3p_(b)#

#a+1/2rhogh=2/3(a+rhogh)#

#a+1/2rhogh=2/3a+2/3rhogh#

#1/3a=(2/3-1/2)rhogh=1/6rhogh#

#h=(2a)/(rhog)=(2*10^5)/(10*10^3)=20m#

The answer is #"option (2)"#