Properties Of Solids And Liquids Question 280

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 [RPET 2000]

Options:

A)10 m

B)20 m

C)60 m

D)30 m

Show Answer

Answer:

Correct Answer: B

Solution:

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) $

therefore $ \frac{1}{3}P _{0}=\frac{1}{6}h\rho g $

therefore $ h=\frac{2P _{0}}{\rho g}=\frac{2\times 10^{5}}{10^{3}\times 10}=20m $ .



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