d
The viscous drag force, \(F = 6\pi \eta rv;\)

\(where\,v = terminal\,velocity\)

\(\therefore \,The\,rate\,of\,production\,of\,heat = power\)

\( = force \times terminal\,velocity\)

\( \Rightarrow power = 6\pi \eta rv \cdot v = 6\pi \eta r{v^2}\,\,\,\,\,\,\,\,...\left( i \right)\)

\(Terminal\,velocity\,v = \frac{{2{r^2}\left( {\rho  - \sigma } \right)}}{{9\eta }};\,\,\,\therefore v \propto {r^2}\)

\(Now,\,power = 6\pi \eta r\left[ {\frac{{4{r^2}{{\left( {\rho  - \sigma } \right)}^2}}}{{81{\eta ^2}}}{g^2}} \right]or\,power \propto {r^5}.\)