In a typical grinding operation, $80 \%$ of the feed material passes through a sieve opening of $4.75 \: \mathrm{mm}$; whereas, $80 \%$ of the ground product passes through $0.5 \: \mathrm{mm}$ opening. If the power required to grind $2 \: \mathrm{tonnes} / \mathrm{h}$ of the feed material is $3.8 \: \mathrm{kW}$, the work index of the material is $\_\_\_\_\_\_\_$ (rounded off to $2$ decimal places)
