MCQ
An air bubble of radius $r$ in water is at a depth $h$ below the water surface at some instant. If $P$ is atmospheric pressure and $d$ and $T$ are the density and surface tension of water respectively. The pressure inside the bubble will be:
  • A
    $\text{P}+\text{h}\rho\text{g}-\big(\frac{4\text{T}}{\text{r}}\big)$
  • B
    $\text{p}+\text{h}\rho\text{g}-\big(\frac{2\text{T}}{\text{r}}\big)$
  • $\text{P}+\text{h}\rho\text{g}+\big(\frac{2\text{T}}{\text{r}}\big)$
  • D
    $\text{P}+\text{h}\rho\text{g}\big(\frac{4\text{T}}{\text{r}}\big)$

Answer

Correct option: C.
$\text{P}+\text{h}\rho\text{g}+\big(\frac{2\text{T}}{\text{r}}\big)$
Excess of pressure inside the air bubble in water $=\frac{\text{2T}}{\text{r}}$
Total pressure inside the air bubble,
$=$ Atmospheric pressure $+$ Pressure due to liquid column $+$ Excess pressure due to $S.T.$
$=\text{p}+\text{h}\rho\text{g}+\big(\frac{2\text{T}}{\text{r}}\big)$

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