Question

Please solve question 153?

Answer 1

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)"`