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Question: If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom on the lake then what...

If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom on the lake then what is the depth of the lake

A

10 m

B

20 m

C

60 m

D

30 m

Answer

20 m

Explanation

Solution

Pressure at bottom of the lake = P0+hρgP _ { 0 } + h \rho g and pressure ay

half the depth of a lake =P0+h2ρg= P _ { 0 } + \frac { h } { 2 } \rho g

According to given condition P0+12hρg=23(P0+hρg)P _ { 0 } + \frac { 1 } { 2 } h \rho g = \frac { 2 } { 3 } \left( P _ { 0 } + h \rho g \right)

⇒ h=2P0ρg=2×105103×10=20 mh = \frac { 2 P _ { 0 } } { \rho g } = \frac { 2 \times 10 ^ { 5 } } { 10 ^ { 3 } \times 10 } = 20 \mathrm {~m}