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

Options

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

Answer

C

Explanation

` P_(1)v_(1) = P_(1)v_(1) + P_(2) v_(2)`
`(4T)/r xx (4pi)/3 r^(3) = (4T)/(r^(1)) xx (4pi)/3 r_(1)^(3) + (4T)/(r_(2))xx (4pi)/3 r_(2)^(3)`
` r^(2) = r_(1)^(2) + r_(2)^(2)`
` r = sqrt(r_(1)^(2) + r_(2)^(2))`