What should be the pressure inside a air bubble of radius 0.1mm situated 1m below the water surface?
(Take surface tension of water T=7.2×10−2N/m and g=10m/s2)
A
3.5×105Pa
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B
1.11×105Pa
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C
2.11×105Pa
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D
3×105Pa
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Solution
The correct option is B1.11×105Pa For air bubble, r=0.1mm=0.1×10−3m=10−4m
Depth of bubble below the water's surface is h=1m
Surface tension of water, T=7.2×10−2N/m.
Pressure at depth h, P1=P0+ρgh P1=105+(1000×10×1)...(i)
Applying equation for excess pressure for air bubble: P2−P1=2Tr...(ii) ∵P2 being on the concave side of bubble, it is higher than P1.
From Eq (i)&(ii), P2−(105+(1000×10×1))=2×7.2×10−210−4 P2=1.1×105+(0.01×105) ∴P2=1.11×105Pa
The pressure inside air bubble is 1.11×105 Pa