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Question

What should be the pressure inside a air bubble of radius 0.1 mm situated 1 m below the water surface?
(Take surface tension of water T=7.2×102 N/m and g=10 m/s2)

A
3.5×105 Pa
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B
1.11×105 Pa
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C
2.11×105 Pa
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D
3×105 Pa
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Solution

The correct option is B 1.11×105 Pa
For air bubble, r=0.1 mm=0.1×103 m=104 m
Depth of bubble below the water's surface is h=1 m
Surface tension of water, T=7.2×102N/m.


Pressure at depth h,
P1=P0+ρgh
P1=105+(1000×10×1) ...(i)
Applying equation for excess pressure for air bubble:
P2P1=2Tr ...(ii)
P2 being on the concave side of bubble, it is higher than P1.


From Eq (i) & (ii),
P2(105+(1000×10×1))=2×7.2×102104
P2=1.1×105+(0.01×105)
P2=1.11×105 Pa
The pressure inside air bubble is 1.11×105 Pa

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