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» <html><body><p>7H<br/>8H<br/>H<br/>2H</p>Solution :If `P_(1)` is the internal <a href="https://interviewquestions.tuteehub.com/tag/pressure-1164240" style="font-weight:bold;" target="_blank" title="Click to know more about PRESSURE">PRESSURE</a> of bubble at the <a href="https://interviewquestions.tuteehub.com/tag/bottom-401202" style="font-weight:bold;" target="_blank" title="Click to know more about BOTTOM">BOTTOM</a> then , <br/>`P_(1)xx(4)/(3)piR_(1)^(3)=P_(2)xx(4)/(3)piR_(2)^(3)`<br/>where `P_(2)` is the <a href="https://interviewquestions.tuteehub.com/tag/excess-978535" style="font-weight:bold;" target="_blank" title="Click to know more about EXCESS">EXCESS</a> pressure inside the bubble at the surface and `R_(2)=2R_(1)`<br/>`P_(1)xx(4)/(3)piR_(1)^(3)=P_(2)xx(4)/(3)pixx8R_(1)^(3)`<br/>`thereforeP_(1)=8P_(2)rArrP_(2)=(P_(1))/(8)`<br/>Pressure at surface `=("pressure at bottom")/(8)`<br/>`H=(H+h)/(8)`<br/> where h= depth of lake <br/> `8H=H+h`<br/>`thereforeh=7H`</body></html>