In a liquid threr is air bubble of radius 1 mm at a depth 10 cm below the free space. The surface tension of liquid `0.075n//m` and density is `1000 kg//m^(2)` . By what amout is the pressure indide the bubble greater than the atmospheric preesure ?

Explanation

Data : ` R = 10^(-3) m , T = 0.072 N//m , p= 10^(3) kg//m^(3) , h= 0.1` m
Let the atmospheric pressure be ` p_(0) ` then , the absolute pressure within the liquid at a depth h is
` p = p_(0) + rhogh`
Hence , the pressure inside the bubble is
` p_("in") = p_(0) + (2T)/R = p_(0) + rhogh+ (2T)/R`
The excess pressure inside the bubble over the atmospheric pressure is
` P_("in") = p_(0) = rhohg + (2T)/R`
` = (10^(3)) (9.8) (0.1) + (2(0.072))/(10^(-3))`
` = 980 + 144 =1124` Pa