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

Answer

B

Explanation

Pressure at bottom of the lake `= P_(0) + h rho g`
Pressure at half the depth of a lake
`= P_(0) + (h)/(2) rho g`
According to given condition
`P_(0)+(1)/(2)h rhog=(2)/(3)(P_(0)+h rhog)rArr (1)/(3)P_(0)=(1)/(6)h rhog`
`rArr h=(2 P_(0))/(rhog)(2P_(0))/(rhog)=(2xx10^(5))/(10^(3)xx10)=20 cm`