JEE Main 2025 Apr 3 Shift 2, Physics Q22: Properties of Fluids

JEE Main2025Apr 3, Shift 2Physics

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 _______.

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Solution

For a soap bubble in air with two surfaces, excess pressure $Δ P = \frac{4 T}{R}$ , so $R \propto \frac{1}{Δ P}$ .

Given $Δ P_{A} = \frac{1}{2} Δ P_{B}$ , we get $\frac{R _{A}}{R _{B}} = \frac{Δ P _{B}}{Δ P _{A}} = 2$ .

Volume scales as the cube of radius: $\frac{V _{A}}{V _{B}} = (\frac{R _{A}}{R _{B}})^{3} = 2^{3} = 8$ .

$∴ n = 8$ .

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JEE Main 2025 Apr 3 Shift 2, Physics Q22: Properties of Fluids

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