Calculate the pressure inside a small air bubble of radus `r` situated at a depth `h` below the free surface of liquids of densities `rho_(1)` and `rho_(2)` and surface tennsions `T_(1)` and `T_(2)`. The thickness of the first and second liquids are `h_(1)` and `h_(2)` respectively. Take atmosphere pressure `=P_(0)`.

Options

A. `P_0+rho_1gh_1+rho_2g(h-h_1)-(2T)/(r )`
B. `P_0+rho_1gh_1+rho_2g(h-h_1)+(2T)/(r )`
C. `P_0+rho_1gh_2+rho_2g(h-h_1)+(2T)/(r )`
D. none of these

Answer

B

Explanation

`P_C=P_B+(2T)/(r )`
`P_B=P_A+rho1gh_1+rho2g(h-h_1)`
where `P_A=P_0`
`P_C=P_0+rhogh_1+rho_2g(h-h_1)+(2T)/(r )`
Then evaluate by putting the numerical values,