JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Fluid Mechanics

There is an air bubble of radius 1.0 mm in a liquid of surface tension

0.075

^{- 1}

and density 1000 kg m

^{- 3}

at a depth of 10 cm below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is ______ Pa (

g = 10

^{- 2}

Answer: 1150

Solution

Inside the air bubble the pressure exceeds atmospheric by the hydrostatic head plus the surface-tension excess,

Δ P = h ρ g + \frac{2 T}{r}

. Here

h ρ g = 0.1 \times 1000 \times 10 = 1000 Pa

and

\frac{2 T}{r} = \frac{2 \times 0.075}{1 0 ^{- 3}} = 150 Pa

. The pressure inside the bubble is greater than atmospheric by

1150 Pa

JEE Main · 2023 · 15 Apr 2023 · Shift 1 · Integer answer

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