Please solve question 153?

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1 Answer
Apr 7, 2018

The answer is "option (2)"

Explanation:

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)"