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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