Properties Of Solids And Liquids Question 319

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) 10m

B) 20m

C) 60m

D) 30m

Show Answer

Answer:

Correct Answer: B

Solution:

Pressure at half the depth $ =P _{0}+\frac{h}{2}dg $

Pressure at the bottom $ =P _{0}+h\rho g $

According to given condition $ P _{0}+\frac{h}{2}dg=\frac{2}{3}(P _{0}+hdg) $

therefore $ 3P _{0}+\frac{3h}{2}dg=2P _{0}+2hdg $

$ \Rightarrow h=\frac{2P _{0}}{dg}=\frac{2\times 10^{5}}{10^{3}\times 10}=20\ m $



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