When a large bubble rises from the bottom of a lake to the surface its radius doubles. If atmospheric pressure is equal to that of column of water height H then the depth of lake is

Options

A. H
B. 2H
C. 7H
D. 8H

Answer

C

Explanation

`r_(2)=2r_(1)" "therefore(V_(2))/(V_(1))=((r_(2))/(r_(1)))^(3)`
`(V_(2))/(V_(1))=8" "thereforeV_(2)=8V_(1)`
`P_(1)V_(1)=P_(2)V_(2)`
`V(P_(0)+H_(1) rho g)=P_(0)8V`
`P_(0)+H rho g=8P_(0)`
`H_(1)rhog=8P_(0)-P_(0)=7P_(0)`
`H_(1)rhog=7H rho g`
`H_(1)=7H`.