Q62 / 75 · JEE Main 2025 (3 Apr Shift 2) · Physics
The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is $n$ times the volume of the bubble $B$, then, the value of $n$ is ___.
Correct answer: 8
Solution
$\begin{aligned} & \Delta \mathrm{P}=\frac{4 \mathrm{~T}}{\mathrm{R}} \\ & \frac{\mathrm{R}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{B}}}=\frac{\Delta \mathrm{P}_{\mathrm{B}}}{\Delta \mathrm{P}_{\mathrm{A}}}=2 \\ & \frac{\mathrm{~V}_{\mathrm{A}}}{\mathrm{V}_{\mathrm{B}}}=\left(\frac{\mathrm{R}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{B}}}\right)^3=8\end{aligned}$
Hence, the correct answer is 8.