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 ${\mathrm{\rho }}_1$ and ${\mathrm{\rho }}_2$ and surface tensions ${\mathrm{T}}_1 \mathrm{and} {\mathrm{T}}_2$. The thickness of first and second liquids are ${\mathrm{h}}_1 \mathrm{and} {\mathrm{h}}_2$. Take atmosphere pressure = ${\mathrm{P}}_0$.

 

• A

  ${\mathrm{P}}_0+{\mathrm{\rho }}_1{\mathrm{gh}}_1+{\mathrm{\rho }}_2\mathrm{g}(\mathrm{h}-{\mathrm{h}}_1)-\frac{2{\mathrm{T}}_2}{\mathrm{r}}$

• B

  ${\mathrm{P}}_0+{\mathrm{\rho }}_1{\mathrm{gh}}_1+{\mathrm{\rho }}_2\mathrm{g}(\mathrm{h}-{\mathrm{h}}_1)+\frac{2{\mathrm{T}}_2}{\mathrm{r}}$

• C

  ${\mathrm{P}}_0+{\mathrm{\rho }}_1\mathrm{g}(\mathrm{h}-{\mathrm{h}}_1)+\frac{2{\mathrm{T}}_2}{\mathrm{r}}$

• D

  ${\mathrm{P}}_0+{\mathrm{\rho }}_1{\mathrm{gh}}_2+{\mathrm{\rho }}_2\mathrm{g}(\mathrm{h}-{\mathrm{h}}_1)+\frac{2{\mathrm{T}}_2}{\mathrm{r}}$