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Question

The pressure inside two soap bubbles are 1.01 and 1.02 atmosphere respectively, then the ratio of their volume:


A
102:101
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B
(102)3:(101)3
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C
8:1
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D
2:1
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Solution

The correct option is C 8:1
Excess pressure in bubble A is 
1.01 - 1 = 0.01 atmosphere
and Excess pressure in bubble B is 
1.02 - 1 = 0.02 atmosphere
By excess pressure formula
$$\Delta P = \dfrac{4T}{R}$$
$$0.01 = \dfrac{4T}{R_A}$$ and 
$$0.02 = \dfrac{4T}{R_B}$$
So, $$\dfrac{R_A}{R_B} = \dfrac{2}{1} $$
Now, volume is proportional to $$(radius)^3$$
$$\therefore \dfrac{V_A}{V_B} = {(\dfrac{R_A}{R_B})}^3 = (\dfrac{2}{1})^3 = \dfrac{8}{1}$$

Physics

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