Fluid Mechanics

JEE Main level, numerical answer, medium

97 of 192

Question 97 of 192

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 nn times the volume of the bubble BB, then, the value of nn is ___.

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Answer: 8

ΔP=4 TRRARB=ΔPBΔPA=2 VAVB=(RARB)3=8\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}

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