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Question

An air bubble of volume V is released from the bottom of a lake which has a depth of 11 m. Find the volume of the bubble at the surface of the lake. The water has density 1000kg/m3. At the release point of the bubble and at the surface, temperature is 4C. The atmospheric pressure is 1.01×105N/m2.

A
12.089V
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B
7.089V
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C
2.089V
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D
8.089V
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Solution

The correct option is C 2.089V
Given : P1=1.01×105 N/m2 V2=V h=11 m ρ=1000 kg/m3
Pressure at a depth h P2=P1+ρgh
P2=1.01×105+1000(10)(11)=2.11×105 N/m2
Using P1V1=P2V2
1.01×105×V1= 2.11×105×V V1=2.089V

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