Calculate the pressure inside a small air bubble of radius r situated at a depth of h below the free surface of liquids of densities $ρ_{1}$ and $ρ_{2}$ and surface tensions $T_{1} and T_{2}$ . The thickness of first and second liquids are $h_{1} and h_{2}$ . Take atmosphere pressure = $P_{0}$ .

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$P_{0} + ρ_{1} {gh}_{1} + ρ_{2} g (h - h_{1}) + \frac{2 T_{2}}{r}$

$P_{0} + ρ_{1} {gh}_{1} + ρ_{2} g (h - h_{1}) - \frac{2 T_{2}}{r}$

$P_{0} + ρ_{1} {gh}_{2} + ρ_{2} g (h - h_{1}) + \frac{2 T_{2}}{r}$

$P_{0} + ρ_{1} g (h - h_{1}) + \frac{2 T_{2}}{r}$

answer is B.

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Detailed Solution

$P_{C} = P_{B} + \frac{2 T}{r}$

$P_{B} = P_{A} + ρ_{1} {gh}_{1} + ρ_{2} g (h - h_{1})$

where $P_{A} = P_{0}$

$P_{C} = P_{0} + ρ_{1} {gh}_{1} + ρ_{2} g (h - h_{1}) + \frac{2 T_{2}}{r}$

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