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Question

An air bubble of radius r in water is at a depth h below the water surface. If P is atmospheric pressure and d and T are the density and surface tension of water respectively. The pressure inside the bubble will be:


A
P+hdg4Tr
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B
P+hdg+2Tr
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C
P+hdg2Tr
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D
P+hdg+4Tr
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Solution

The correct option is C $$\displaystyle P+hdg+\frac{2T}{r}$$
Pressure just outside the bubble will be $$ P + hdg $$
The $$ 2T/r $$ component is due to water-air interface surface tension and is additive because water exerts pressure on the bubble
So total pressure =  $$ P + hdg + 2T/r$$

Physics

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