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An air bubble doubles in radius on strin...

An air bubble doubles in radius on string from the bottom of a lake to its surface. If the atmospheric pressure is equal to that of a column of water of height `H`, the depth of the lake is

A

H

B

2 H

C

7 H

D

8 H

Text Solution

Verified by Experts

The correct Answer is:
B
At the surface of the lake, only the atmospheric pressure (H) acts on the air bubble.
While at a depth h below the water surface, the pressure=atomospheric pressure+hydrostatic pressure=H+h
`:.` Using Boyle's law, we get
`P_1V_1=P_2V_2`
`:." "Hxx4/3pi(2R)^3=(H+h)xx4/3piR^3`
`:.` 8H=H+h
`:.` h=8H-H=7H
Thus the depth of the lake=7H
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