Q127 / 150 · MHT CET 2023 (11 May Shift 2) · Physics
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 $\left.=3.2 \times 10^{-2} \mathrm{Nm}^{-2}\right]$
- A$2 \mathrm{~cm}$
- B$1.5 \mathrm{~cm}$
- Correct answerC$1 \mathrm{~cm}$
- D$0.5 \mathrm{~cm}$
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, $2 \mathrm{R}=1 \mathrm{~cm}$
Hence, the correct answer is option: 'C'.