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

Options

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

Answer

a

Explanation

If `P_(1)` is the internal pressure of bubble at the bottom then ,
`P_(1)xx(4)/(3)piR_(1)^(3)=P_(2)xx(4)/(3)piR_(2)^(3)`
where `P_(2)` is the excess pressure inside the bubble at the surface and `R_(2)=2R_(1)`
`P_(1)xx(4)/(3)piR_(1)^(3)=P_(2)xx(4)/(3)pixx8R_(1)^(3)`
`thereforeP_(1)=8P_(2)rArrP_(2)=(P_(1))/(8)`
Pressure at surface `=("pressure at bottom")/(8)`
`H=(H+h)/(8)`
where h= depth of lake
`8H=H+h`
`thereforeh=7H`