When air bubble comes from bottom to the top of a lake its radius becomes n times. If temprerature remains constant through out the lake the depth of the lake will be.

Explanation

From Boyle's law `PV=` constant`impliesP_(1)V_(1)=P_(2)V_(2)`
`(P_(0)+hrhog+(2T)/(R))^(4)/(3)piR^(3)=(P_(0)+(2T)/(nR))(4)/(3)pi(nR)^(3)`
`hrhog=P_(0)(n^(3)-1)+(2T)/(nR)n^(3)-(2T)/(R)`
`h=(P_(0)(n^(3)-1)+(2T)/(R)[n^(2)-1])/(rhog)`