The amount of work done in blowing a soap bubble such that its diameter increases from d to D is (T=surface tension of the solution)

Options

A. `2pi (D^2 - d^2) T`
B. `2pi (D - d) T`
C. `2pi (D - d)T^2`
D. `2pi ( D+ d) T^2`

Answer

A

Explanation

An air bubble has two surfaces .
Initial surface area ` = 2 xx 4pi (d/2)^2 = 2pi d^2`
Final surface area ` = 2 xx 4pi (D/2)^1 = 2pi D^2`
Change in area ` = 2pi (D^2 - d^2)`
Work done = T x change in area
`W = T xx 2pi (D^2 - d^2) = 2pi (D^2 - d^2) T`