When two soap bubbles of radius `r_(1) " and " r_(2)(r_(2) gt r_(1))` coalesce, the radius of curvature of common surface is

Options

A. `(r_(2) - r_(1))`
B. `(r_(2) + r_(1))`
C. `(r_(2) - r_(1))/(r_(1)r_(2))`
D. `(r_(1)r_(2))/(r_(2) - r_(1))`

Answer

D

Explanation

The excess pressure inside the first bubble of radius `r_(1)` is `p_(1) = 4S//r_(1)` and in the second bubble of radius `r_(2)` is `p_(2) = 4S//r_(2)`.
`:.` Excess pressure, `p = (4S)/(r) = (4S)/(r_(1)) - (4S)/(r_(2))`

`rArr (1)/(r) = (r_(2) - r_(1))/(r_(1)r_(2)) rArr r = (r_(1)r_(2))/(r_(2) - r_(1))`