Pressure inside two soap bubbles are 1.01 and 1.02 atmospheres. Ratio between their volumes is

Question

Pressure inside two soap bubbles are 1.01 and 1.02 atmospheres. Ratio between their volumes is (A)  2:1  (B)  8:1  (C)  108:101  (D) (102)2:(103)2

Tardigrade Admin · Accepted Answer

From the question we have
Excess pressure inside Ist bubble is

= (1.01 - 1)

atmosphere

= 0.01

atmosphere
Excess pressure inside IInd bubble is

= (1.02 - 1) = 0.02

atmosphere
While we know excess pressure are given by

\frac{4 T}{r _{1}}

and

\frac{4 T}{r _{2}}

respectively
So,

\frac{\frac{4 T}{r _{1}}}{\frac{4 T}{r _{2}}} = \frac{0.01}{0.02}

or

\frac{r _{2}}{r _{1}} = \frac{1}{2}

Let volumes of first and second bubbles are

V_{1}

and

V_{2}

respectively
So,

\frac{V _{1}}{V _{2}} = \frac{\frac{4}{3} π r _{1}^{3}}{\frac{4}{3} π r _{2}^{3}}

= (\frac{r _{1}}{r _{2}})^{2} = (\frac{2}{1})^{3} = \frac{8}{1}

Hence,

V_{1} : V_{2} = 8 : 1

Q. Pressure inside two soap bubbles are $1.01$ and $1.02$ atmospheres. Ratio between their volumes is