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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 
$$ \triangle p_1 = 1.01 - 1 = 0.01 atm $$
Inside bubble B is 
$$ \triangle p_2 = 1.03 - 1 = 0.03 atm $$
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 
$$ p = \dfrac {4t}{r} $$$
Let $$r_1$$ be the radii of bubbles A and B respectively then
 
$$ \dfrac {p_1}{p_2} = \dfrac { 4T / r_1} { 4T / r_2} = \dfrac {0.01}{0.03} $$

$$ \dfrac {r_2}{r_1} = \dfrac {1}{3} $$
Since bubbles are spherical in shape their volume's are in the ratio 

$$ \dfrac {v_1}{v_2} = \dfrac {\dfrac{4}{2} \pi r_1^3}{\dfrac{4}{3} \pi r_1^3} $$

$$ \left( \dfrac {r_1}{r_2} \right)^3  = \left( \dfrac {3}{1} \right)^3 = \dfrac {27}{1} $$

$$ V_1 : V_2 = 27 : 1 $$

Physics

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