The work done in blowing a bubble of volume `V` is `W`, then what is the work done in blowing a soap bubble of volume `2V` ?

Options

A. `W//2`
B. `sqrt(2)W`
C. `.^(3)sqrt(2)W`
D. `.^(3)sqrt(4)W`

Answer

D

Explanation

As volume of the bubble `V=(4)/(3) pi R^(3) implies R = ((3)/(4pi))^(1//3)V^(1//3) implies R^(2) = ((3)/(4pi))^(2//3) V^(2//3) implies R^(2) prop V^(2//3)`
Work done in blowing a soap bubble `W = 8piR^(2)T implies W prop R^(2) prop V^(2//3)`
`therefore (W_(2))/(W_(1)) = ((V_(2))/(V_(1)))^(2//3) = ((2V)/(V))^(2//3) = (2)^(2//3) = (4)^(1//3) implies W_(2) = .^(3)sqrt(4)W`