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When two soap bubbles of radii r1 and r2...

When two soap bubbles of radii `r_1 and r_2 (r_2 lt r_1)` adjoin, the radius of curvature of the common surface is

A

`r_2-r_1`

B

`r_2+r_1`

C

`((r_2-r_1))/(r_1r_2)`

D

`(r_1r_2)/(r_2-r_1)`

Text Solution

Verified by Experts

The correct Answer is:
D
If the atmospheric pressure is `p_0` , then in case of the first bubble,
`p_1-p_0=(4T)/(r_1) [ T=` surface tension of soap solution]
In case of the second bubble,
`p_2-p_0=(4T)/(r_2)`
`therefore p_1-p_2=4T(1/r_1-1/r_2)`
Again, if the radius of curvature of the common surface is r, then , `p_1-p_2=(4T)/(r )`
`therefore (4T)/(r )= 4T(1/r_1-1/r_2) or, 1/r=(r_2-r_1)/(r_1r_2) or, r=(r_1r_2)/(r_2-r_1)`
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