Radius of an air bubble at the bottom of the lake is `r` and it becomes `2 r` when the air bubbles rises to the top surface of the lake. If P cm of water be the atmospheric pressure, then the depth of the lake is

Options

A. 2p
B. 8p
C. 4p
D. 7p

Answer

D

Explanation

let depth of lake is x cm.
`thereforep_(1)V_(1)=p_(2)V_(2)`
`(pdg+xdg)((4)/(3)pir^(3))`
`=pdg[(4)/(3)pi)(2r)^(3)]`
`(p+x)r^(3)=p(8r^(3))`
`x=8p-p`
`impliesx=7p`