Question

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 ${\rho }_1$ and ${\rho }_2$ and surface tensions $T_1$ and $T_2$. The thickness of first and second liquids are $h_1$ and $h_2$. Take atmosphere pressure $=P_0$

• A. $P_0+{\rho }_{1}g{h}_1+{\rho }_{2}g(h-h_1)-\frac{2T_2}{r}$
• B. none of these
• C. $P_0+{\rho }_{1}g{h}_1+{\rho }_{2}g(h-h_1)+\frac{2T_2}{r}$
• D. $P_0+{\rho }_{1}g{h}_2+{\rho }_{2}g(h-h_1)+\frac{2T_2}{r}$

Answer 1

The correct option is C $P_0+{\rho }_{1}g{h}_1+{\rho }_{2}g(h-h_1)+\frac{2T_2}{r}$

Given,
$P_A=P_o$
$P_C=P_B+\frac{2T}{r}$

$P_B=P_A+{\rho }_{1}g{h}_1+{\rho }_{2}g(h-h_1)$

Hence,
$P_C=P_0+{\rho }_{1}g{h}_1+{\rho }_{2}g(h-h_1)+\frac{2T_2}{r}$

Final answer: (b)