Question

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

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

Solution

## The correct option is C 8:1Excess pressure in bubble A is 1.01 - 1 = 0.01 atmosphereand Excess pressure in bubble B is 1.02 - 1 = 0.02 atmosphereBy 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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