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 $ .
