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. 70 m
• B. 40 m
• C. 20 m
• D. 60 m

Answer 1

The correct option is C 20 m

Pressure at bottom of the lake$=P_0+h\rho g{P}_0+\frac{h}{2}\rho g$

According to Guro condition:

$\frac{1}{3}{P}_0=\frac{1}{6}h\rho g\Rightarrow h=\frac{2P_0}{\rho g}=\frac{2\times {10}^5}{{10}^3\times 10}=20m$

Pressure at depth of lake$\Rightarrow$

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