Question

If pressure at half the depth of a lake is equal to 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

Pressure at bottom of the lake = $P_0+h\rho g$

Pressure at half the depth of a lake = $P_0+\frac{h}{2}\rho g$

According to given condition

$P_0+\frac{1}{2}h\rho g=\frac{2}{3}(P_0+h\rho g)\Rightarrow \frac{1}{3}{P}_0=\frac{1}{6}h\rho g$

$\Rightarrow h=\frac{2P_0}{\rho g}=\frac{2\times {10}^5}{{10}^3\times 10}=20m$