A soap bubble in vacuum has a radius of 3cm & another soap bubble in vacuum has a radius of 4 cm if the 2 bubbles coalesce under isothermal conditions then what is radius of the new bubble ?

Explanation

Pressure inside the bubble in vacuum `rho = (4S)/(r )`
Volume of bubble, `V = (4)/(3) pi r^(3)`
as PV = a constant
`(4s)/(R ) xx (4)/(3) pi r^(3) = (4S)/(r_(1)) xx (4)/(3)pir_(1)^(3) + (4S)/(r_(2)) xx (4)/(3)pi r_(2)^(3)`
or `R^(2) = r_(1)^(2) + r_(2)^(2)`
`= 3^(2) + 4^(2) = 25`
`R = 5 cm`