The radii of two soap bubbles are `r_(i)` and `r_(2)`. In isothermal conditions, two meet together in vacuum. Then the radius kof the resultant bubble is given by

Options

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

Answer

C

Explanation

Under isothermal conditions , the total energy (work done in blowing ) remains constant ,
` :. ` Work done = Energy stored ` = 8piR^(2)T`
` :. 8pir_(1)^(2)T + 8piR^(2)T`
` :. r_(1)^(2) + r_(2)^(2)=R^(2) " " :. R = (r_(1)^(2) + r_(2)^(2)) ^(1//2)`