Power = rate of production of heat = F.V

= 6\pi $$\eta rV_T.V_T = = 6\pi $$\eta rV_T²

[ As F = 6\pi $$\eta rV_T from stoke’s formula ]

$\because$ Terminal velocity V_T = ${{2{r^2}\left( {\rho - \sigma } \right)g} \over {9\eta }}$

$\therefore$ V_T $\propto$ r²

$\therefore$ Power $\propto$ 6\pi $$\eta r$\left[ {{{4{r^4}{{\left( {\rho - \sigma } \right)}^2}{g^2}} \over {81{\eta ^2}}}} \right]$

$\Rightarrow$ Power $\propto$ r⁵