A soup bubble in vacume has a redius `3cm ` and another soup bubble in vacume has radius `4cm` If two bubble coulese under isothermal condition , then the radius of the new bubble will be

Options

A. `7 cm`
B. `5 cm`
C. `4.5 cm`
D. `2.3 cm`

Answer

b

Explanation

An isothermal process obeys boy's law since process is isothermal the total pressure of inside the bubble is same as excess of pressure given by
`P = (4T)/(R),`
where T is surface tension and R radius also an isothermal precess obeys boy's law Hence, `PV = "constant"` Let R be the ratio of conlesce system then
`P_(1)V_(1) + P_(2)V_(2) = PV`
`((4T)/(R_(1))) ((4)/(3) pi R^(2)) + ((4T)/(R_(2))) ((4)/(3) pi R_(2)^(1)) = ((4T)/(R))((4)/(3) pi R^(2))`
`rArr r_(1)^(2) + r_(2)^(2) = R`
Given `R_(1) = 3 cm` and `R_(2) = 4 cm`
`:. R = sqrt(3^(2) + 4^(2))`
`R = 5 cm`