Two separate air bubbles (radii `0.002 cm` and `0.004`) formed of the same liquid (surface tension `0.07 N//m`) come together to form a double bubble. Find the radius and the sense of curvature of the internal film surface common to both the bubbles.

Answer

D

Explanation

`p_(1)=p_(0)+(4T)/(r_(1)) implies p_(2)=p_(0)+(4T)/(r_(2))`
`r_(2) ltr_(1)`
`:. p_(2)gtp_(1)`
i.e. pressure inside the smaller bubble will be more. The excess pressure

`p= p_(2)-p_(1)=4T((r_(1)-r_(2))/(r_(1)r_(2)))` ...(i)
This excess pressure acts from concave to convex side, the interface will be concave towads smaller bubble and convex towareds larger bubble. Let R be the radius of interface then,
`p=(4T)/(R) `...(ii)
From Eqs, (i) and (ii), we get
`R=(r_(1)r_(2))/(r_(1)-r_(2))=((0.004)(0.002))/((0.004-0.002)`
`=0.004 m`