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Question

Pressure inside two soap bubbles are 1.01 atm and 1.03 atm. Ratio between their volumes is :

A
27 : 1
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B
3 : 1
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C
127 : 101
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D
None of these.
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Solution

The correct option is A 27 : 1
Excess pressure as compared to atmosphere inside bubble A is
p1=1.011=0.01atm
Inside bubble B is
p2=1.031=0.03atm
Also when radius of a bubble is r, formed from a solution whose surface tension is t, then excess pressure inside the bubble is given by
p=4tr$
Let r1 be the radii of bubbles A and B respectively then
p1p2=4T/r14T/r2=0.010.03

r2r1=13
Since bubbles are spherical in shape their volume's are in the ratio

v1v2=42πr3143πr31

(r1r2)3=(31)3=271

V1:V2=27:1

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