Find the pressure in a bubble of radius 0.2 cm formed at the depth of 5cm from the free surface of water . The surface tension of water is 70 dyne cm^(-1) and its density is 1gcm^(-3) . Atmospheric pressure is 10^(6) dyne cm^(-2) .The gravitational acceleration is 980cms^(-2).

Find the pressure in a bubble of radius 0.2 cm formed at the depth of

1.	Find the pressure in a bubble of radius 0.2 cm formed at the depth of 5cm from the free surface of water . The surface tension of water is 70 dyne cm^(-1) and its density is 1gcm^(-3) . Atmospheric pressure is 10^(6) dyne cm^(-2) .The gravitational acceleration is 980cms^(-2).
Answer» <P> SOLUTION :`{:(h=5cm,R=0.2cm),(T=70 "dyne " cm ^(-1),rho=1gcm^(-3)),(P=10^(6) "dyne" cm^(-2),g=980 cm-s^(-2)):}` If the pressures inside and outside of the AIR bubble FORMED in water are `P_(i)andP_(o)`respectively , `P_(i)-P_(o)=(2T)/(R)` (A bubble in water has one free surface only.) `thereforeP_(i)=P_(o)+(2T)/(R)` ...(1) But `P_(o)=` atmmospheric pressure + pressure due to watarcolumn of height h. `thereforeP_(o)=P+hrhog` ...(2) From equations (1)and (2), `P_(i)=P+hrhog+(2T)/(R)` `=10^(6)+(5xx1xx980)+(2xx70)/(0.2)` `=10^(6)+4900+700` `P_(i)=1.0056xx10^(6)"dyne " cm^(-2)