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Calculate the pressure inside a small ai...

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)`.

A

`P_(0)+rho_(1)gh_(1)+rho_(2)g(h-h_(1))-(2T_(2))/r`

B

`P_(0)+rho_(1)gh_(1)+rho_(2)g(h-h_(1))+(2T_(2))/r`

C

`P_(0)-rho_(1)gh_(2)+rho_(2)g(h-h_(1))+(2T_(2))/r`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`P_C=P_B+(2T)/r`
`P_B=P_A+rho_1g_1=rho-2g(h-h_1)`

where `P_A=P_0`
`P_C=P_0+rho_1gh_1+rho_2g(h-h_1)+(2T_2)/r`
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