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 ?

Options

A. `10m`
B. `20m`
C. `60m`
D. `30m`

Answer

B

Explanation

Pressure at half depth`=P_0+(h)/(2)dg`
Pressure at the bottom`=P_0+hrhog`
According to given condition
`P_0+(h)/(2)dg=(2)/(3)(P_0+hdg)`
`implies3P_0+(3h)/(2)dg=2P_0+2hdg`
`impliesh=(2P_0)/(dg)=(2xx10^5)/(10^3xx10)=20m`