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Q.
The ratio of radii of two soap bubbles is $2 : 1$. The ratio of excess pressures inside them is
UP CPMTUP CPMT 2012Mechanical Properties of Fluids
Solution:
Excess pressure inside the soap bubble is
$P=\frac{4T}{R}$
where $T$ is the surface tension of the soap solution and $R$ is the radius of the bubble.
$\therefore P_{1}=\frac{4T}{R_{1}}\quad\ldots\left(i\right)$
and $P_{2}=\frac{4T}{R_{2}}\quad\ldots\left(ii\right)$
Divide $\left(i\right)$ by $\left(ii\right)$, we get
$\frac{P_{1}}{P_{2}}=\frac{R_{2}}{R_{1}}=\left(\frac{1}{2}\right)\quad$ $\left(\because \frac{R_{1}}{R_{2}}=\frac{2}{1}\left(\text{Given}\right)\right)$