Two soap bubble of different radii `R_(1)` and `R_(2) (ltR_(1))` coalesce to form an interface of radius R as shown in figure. The correct value of R is
.

Options

A. `R=R_(1)-R^(2)`
B. `R=(R_(1)-R^(2))/(2)`
C. `(1)/(R)=(1)/(R_(2))-(1)/(R_(1)`
D. `(1)/(R)=(1)/(R_(2))+(1)/(R_(1))`

Answer

C

Explanation

`(p_(2)-p_(1))=(4T)/(R )`
Where `R =`radius of common surface
`:. (4T)/(R^(2))-(4T)/(R^(1))=(4T)/(R )`
`(1)/(R)=(1)/(R_(2))-(1)/(R_(1))`.