Radius of a soap bubble is increased from R to 2R. Work done in this process in terms of surface tension S is

Options

(a) 24 πR²S
(b) 48 πR²S
(c) 12 πR²S
(d) 36 πR²S

Correct Answer:

24 πR²S

Explanation:

Work done = 2 x S x Change in surface area
W = 2 x S x 4π (R₂² – R₁²)
Given: R₂ = 2R, R₁ = R = 8S π (4R² – R²) = 24 πR²S.