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Q)

Excess pressure inside one soap bubble is three times that inside second soap bubble. Find the ratio of volume of first bubble to second.

\[\begin {array} {1 1} (a)\;\frac{1}{25} \\ (b)\;\frac{1}{27} \\ (c)\;\frac{1}{4}\\ (d)\;\frac{1}{8} \end {array}\]

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A)
$P_1= \large\frac{4T}{r_1}$
$P_2= \large\frac{4T}{r_2}$
$\large\frac{P_1}{P_2}=\frac{r_2}{r_1}$
$\large\frac{r_2}{r_1}$$=3$
$r_2=3r_1$
ratio of volumes
$\large\frac{V_1}{V_2}=\frac{\Large\frac{4 \pi}{3} r_1^3}{\Large\frac{4 \pi}{3}r_2^3}$
$\qquad= \bigg(\large\frac{r_1}{r_2}\bigg)^3$
$\qquad=\bigg(\large\frac{1}{3}\bigg)^3$
$\qquad= \large\frac{1}{27}$
Hence b is the correct answer.

 

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