A steel sphere of radius $0\mathrm{.}1$ m at $400$K is immersed in an oil at $300$K$.$ If the centre of the sphere reaches $350$K in $20$ minutes, how long will it take for a $0\mathrm{.}05$ m radius steel sphere to reach the same temperature $($at the centre$)$ under identical conditions? Assume that the conductive heat transfer co$-$efficient is infinitely large.

$5$ minutes

$10$ minutes

$20$ minutes

$40$ minutes