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Two spherical soap bubbles of radii r1 a...

Two spherical soap bubbles of radii `r_1` and `r_2` in vacuume collapse under isothermal condition. The resulting bubble has radius `R` such that

A

`sqrt(r_1r_2)`

B

`sqrt(r_1^2+r_2^2)`

C

`(r_1r_2)/(r_1+r_2)`

D

`(r_1+r_2)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`P_0=0`

`P_1=P_0+(4T)/(r_1),P_2=P_0+(4T)/r_2,P=P_0+(4T)/r`
And `n_1+n_2=n`
`implies (P_1V_1)/(RT)=(P_2V_2)/(RT)=(PxxV)/(RT)`
`implies r_1^2+r_2^2=r^2`
`implies r= sqrt(r_1^2+r_2^2)`
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