JEE Main 2025 Jan 23 Shift 2, Physics Q21: Properties of Fluids

JEE Main2025Jan 23, Shift 2Physics

An air bubble of radius $1.0$ mm is observed at a depth of $20$ cm below the free surface of a liquid having surface tension $0.095 J / m^{2}$ and density $1 0^{3} k g / m^{3}$ . The difference between pressure inside the bubble and atmospheric pressure ______ $N / m^{2}$ . (Take $g = 10 m / s^{2}$ )

Your answer

Solution

Two pressure contributions add up between the atmosphere and the inside of the bubble.

Hydrostatic increase from the surface to depth $h$ : $ρ g h$ .

Laplace (surface-tension) jump across the single liquid $-$ air interface of a bubble inside a liquid: $\frac{2 T}{R}$ .

$Δ P = P_{in} - P_{0} = ρ g h + \frac{2 T}{R} .$

Substitute $ρ = 1 0^{3}, g = 10, h = 0.20, T = 0.095, R = 1 0^{- 3}$ :

$ρ g h = 1 0^{3} \cdot 10 \cdot 0.20 = 2000 N / m^{2} .$

$\frac{2 T}{R} = \frac{2 \times 0.095}{1 0 ^{- 3}} = 190 N / m^{2} .$

$Δ P = 2000 + 190 = 2190 N / m^{2} .$

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JEE Main 2025 Jan 23 Shift 2, Physics Q21: Properties of Fluids

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