Surface energy of soap bubble :

\(U=T \times 4 \pi r^2\)

\(U_1=T \times 4 \pi(\frac{r}{2})^2=T \times 4 \pi (\frac{r^2}{4}) =\pi T r^2\)

\(U_2=T \times 4 \pi(2 r)^2=16 \pi T r^2\)

The work done in increasing the radius of soap bubble is equal to the increase in surface energy.

\(\therefore W =\left( U _2- U _1\right)\)

\(=16 \pi Tr ^2-\pi Tr ^2\)

\(=15 \pi Tr ^2\)

Thus, the work done in increasing the radius of soap bubble will be \(=15 \pi Tr ^2\)