An air bubble of radius 0.1, cm is in a liqui | vedclass

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(A) Given: Radius of air bubble,$r = 0.1\, cm = 10^{-3}\, m$.Surface tension of liquid,$S = 0.06\, N/m = 6 	imes 10^{-2}\, N/m$.Density of liquid,$

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$0.1$

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(A) Given: Radius of air bubble,$r = 0.1\, cm = 10^{-3}\, m$.Surface tension of liquid,$S = 0.06\, N/m = 6 	imes 10^{-2}\, N/m$.Density of liquid,$ho = 10^3\, kg/m^3$.Excess pressure inside the bubble,$P_{excess} = 1100\, N/m^2$.Depth of bubble below the liquid surface,$h = ?$.The total pressure inside the bubble at depth $h$ is given by $P_{in} = P_{atm} + hho g + \frac{2S}{r}$.The excess pressure over atmospheric pressure is $P_{excess} = P_{in} - P_{atm} = hho g + \frac{2S}{r}$.Substituting the values: $1100 = h 	imes 10^3 	imes 9.8 + \frac{2 	imes 6 	imes 10^{-2}}{10^{-3}}$.$1100 = 9800h + 120$.$9800h = 1100 - 120 = 980$.$h = \frac{980}{9800} = 0.1\, m$.

An air bubble of radius $0.1\, cm$ is in a liquid having surface tension $0.06\, N/m$ and density $10^3\, kg/m^3$. The pressure inside the bubble is $1100\, N/m^2$ greater than the atmospheric pressure. At what depth $h$ (in $m$) is the bubble below the surface of the liquid? $(g = 9.8\, m/s^2)$

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