A soap bubble of radius `r` is placed on another bubble of radius `2r`. The radius of the surface common to both the bubbles is

Options

A. `2r` concave towards `P`
B. `2r` concave towards `Q`
C. `3r` concave towards `P`
D. `3r` concave towards `Q`

Answer

A

Explanation

Excess of pressure in two soap bubbles are
`p_(P)=(4T)/r`
and `p_(Q)=(4T)/(2r)=(2T)/r`
`:.` Pressure difference `Deltap=P_(P)-P_(Q)`
`=(4T)/r-(2T)/r=(2T)/r`
Let radius of curvature of common interface is `R` then
`(4T)/R=(2T)/r=(2T)/r`
Let radius of curvature of common interface is `R` then
`(4T)/R=(2T)/rimpliesR=2r`
Excess of pressure is higher in `P`, so interface will concave towards `P`.