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Q.
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?
NTA AbhyasNTA Abhyas 2022
Solution:
Pressure at bottom of the lake $= \text{P}_{0} + \text{h} \rho \text{g}$
and pressure at half the depth of a lake
$= \text{P}_{0} + \frac{\text{h}}{2} \rho \text{g}$
According to given condition
$= \left(\text{P}\right)_{0} + \frac{1}{2} \rho \text{g} = \frac{2}{3} \left(\left(\rho \right)_{0} + \text{h} \rho \text{g}\right)$
$⇒ \text{h} = \frac{2 \text{P}_{0}}{\rho \text{g}} = \frac{2 \times 1 0^{5}}{1 0^{3} \times 1 0} = 2 0 \text{m}$