JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Fluid Mechanics

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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 ____.

Answer: 8

Solution

The excess pressure inside a soap bubble is

Δ P = \frac{4 T}{R}

, varying inversely with radius. The condition

Δ P_{A} = \frac{1}{2} Δ P_{B}

gives

\frac{4 T}{R _{A}} = \frac{1}{2} \frac{4 T}{R _{B}}

, hence

R_{A} = 2 R_{B}

. Since volume scales as the cube of the radius,

\frac{V _{A}}{V _{B}} = (\frac{R _{A}}{R _{B}})^{3} = 8

, so

n = 8

JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Integer answer

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