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Question

# The excess pressure inside the first soap bubble is three times that inside the second bubble. Then, the ratio of the volume of the first bubble to that of the second bubble will be

A
1:27
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B
3:1
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C
1:3
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D
1:9
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Solution

## The correct option is A 1:27Let us suppose, radius of first and second soap bubble is r1 and r2 respectively. Also suppose, T is surface tension. Now, excess pressure inside first bubble, p1=4Tr1 .......(1) and excess pressure inside second bubble, p2=4Tr2 .......(2) Given, p1=3p2 4Tr1=3×4Tr2 [ from (1) and (2) ] ⇒r1r2=13 .......(3) Ratio of their volumes, V1V2=43πr3143πr32 ⇒V1V2=(r1r2)3=127 [ from (3) ]

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