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Question

An air bubble of volume V0 is released by a fish at a depth h in a lake. The bubble rises to the surface. Assume constant temperature and standard atmospheric pressure P above the lake. The volume of the bubble just before touching the surface will be (density of water is ρ)
(Assume that the radius of bubble is neglegible)

A
V0
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B
V0(ρghP)
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C
V0(1+ρghP)
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D
V0(1+ρghP)
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Solution

The correct option is D V0(1+ρghP)
According to Boyle's law, [at constant temperature]
PV= constant
From the diagram, we can say that,
P1V1=P2V2


Given, P is the atmospheric pressure at the top of the lake. Let the volume of the bubble just before touching the surface be V and volume of the bubble at depth h of the lake be V0.
Then from P1V1=P2V2
(P+hρg)V0=PV
V=(P+hρgP)V0
V=V0[1+ρghP]
Thus, option (d) is the correct answer.

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