There is an air bubble of radius 1.0 mm in a liquid of surface… | JEE Main 2023 (15 Apr, Shift 1)

Q36JEE Main 2023 · 15 APR · SHIFT 1Medium

Excess Pressure: Drops & Bubbles

There is an air bubble of radius $1.0\text{ mm}$ in a liquid of surface tension $0.075\text{ N m}^{-1}$ and density $1000\text{ kg m}^{-3}$ at a depth of $10\text{ cm}$ below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _________ $\text{Pa}\left(g = 10\text{ m s}^{-2}\right)$

Numerical answer type. Work it out, then open the answer.

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Answer: 1150

Air bubble in liquid: $P_{in} - P_0 = h\rho g + \frac{2T}{r}$ .
$h\rho g = 0.1 \times 1000 \times 10 = 1000\text{ Pa}$
$\frac{2T}{r} = \frac{2 \times 0.075}{10^{-3}} = 150\text{ Pa}$
Excess pressure $= 1000 + 150 = 1150\text{ Pa}$

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