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 $[RPET=2000]$

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

Answer 1

Answer: (B)

$20$ m

The Pressure at bottom of the lake = $P_0+h\rho g$
The Pressure at half the depth of a lake = $P_0+\frac{h}{2}\rho g$
According to given condition
$P_0+\frac{1}{2}h\rho g=\frac{2}{3}(P_0+h\rho g)\Rightarrow \frac{1}{3}{P}_0=\frac{1}{6}h\rho g$
$h=\frac{2P_0}{\rho g}=\frac{2\times {10}^5}{{10}^3\times 10}=20m$