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 columnof water of height H. What is the depth of the lake ?

When a large bubble rises from the bottom of a lake to the surface , i

1.	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 columnof water of height H. What is the depth of the lake ?
Answer» 7H 8H H 2H Solution :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`