What should be the diameter of a soap bubble, in order that the excess pressure inside it is $25.6…

What should be the diameter of a soap bubble, in order that the excess pressure inside it is $25.6 \mathrm{Nm}^{-2}$ ? [surface tension of soap solution $\left.=3.2 \times 10^{-2} \mathrm{Nm}^{-2}\right]$
  1. $2 \mathrm{~cm}$
  2. $1.5 \mathrm{~cm}$
  3. $1 \mathrm{~cm}$
  4. $0.5 \mathrm{~cm}$

Solution

The formula for excess pressure inside the bubble is given as $P_0=\frac{4 T}{R}$ Where, $\mathrm{T}$ is surface tension and $\mathrm{R}$ is the radius of the sphere Rearranging the formula for $\mathrm{R}$ and substituting the values,$\begin{aligned} & R=\frac{4 T}{P_0} \\ & R=\frac{4 \times 3.2 \times 10^{-2}}{25.6} \\ & R=0.5 \times 10^{-2} \mathrm{~m}=0.5 \mathrm{~cm} \end{aligned}$ The diameter then becomes, $2 \mathrm{R}=1 \mathrm{~cm}$

Asked in: MHT CET 2023 (11 May Shift 2)

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