Question

If pressure at half the depth of a lake is equal to $\frac{2}{3}$ pressure at the bottom of the lake then what is the depth of the lake?

• A. 10 m
• B. 20 m
• C. 60 m
• D. 30 m

Answer 1

The correct option is B 20 m

The correct option is B

We know that the pressure exerted by a liquid is written as

$P=h\rho g$

now, let the pressure at the half depth of the lake be $P_1=P_0+h_1\rho g$

The pressure at the bottom of the lake is $P_2=P_0+h_2\rho g$

Here, $P_0$ is the atmospheric pressure

so, as given

$P_1=\left(\frac{2}{3}\right)P_2$

or

$P_0+h_1\rho g=\left(\frac{2}{3}\right)(P0+h_2\rho g)$

and $h_1=\frac{h_2}{2}$

so,

$\left(\frac{1}{3}\right)P_0=\left(\frac{1}{6}\right)h_2\rho g$

$h_2=\frac{2P0}{\rho g}$

$h_2=\frac{(2\times 105)}{104}$

The depth of the lake is

$h_2=20m$