SATHEE: Properties Of Solids And Liquids Question 311

Properties Of Solids And Liquids Question 311

Question: Pressure inside two soap bubbles are 1.01 and 1.02 atmospheres. Ratio between their volumes is [MP PMT 1991]

Options:

A) 102 : 101

B) ${(102)}^{3} : {(101)}^{3}$

C) 8 : 1

D)2 : 1

Show Answer

Answer:

Correct Answer: C

Solution:

Outside pressure = 1 atm Pressure inside first bubble = 1.01 atm Pressure inside second bubble = 1.02 atm

Excess pressure $Δ P_{1} = 1.01 - 1 = 0.01$ atm

Excess pressure $Δ P_{2} = 1.02 - 1 = 0.02$ atm $Δ P \propto \frac{1}{r} \Rightarrow r \propto \frac{1}{Δ P} \Rightarrow \frac{r_{1}}{r_{2}} = \frac{Δ P_{2}}{Δ P_{1}} = \frac{0.02}{0.01} = \frac{2}{1}$ Since $V = \frac{4}{3} π r^{3} ∴ \frac{V_{1}}{V_{2}} = {(\frac{r_{1}}{r_{2}})}^{3} = {(\frac{2}{1})}^{3} = \frac{8}{1}$

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Properties Of Solids And Liquids Question 311

Question: Pressure inside two soap bubbles are 1.01 and 1.02 atmospheres. Ratio between their volumes is [MP PMT 1991]

Options:

Answer:

Solution:

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